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SAT Exam  >  SAT Questions  >  The cost of 2 pencil, 4 pens and 8 erasers is... Start Learning for Free
The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8 pens, 10 pencils and 4 erasers is Rs. 36. How much will 3 pencils, 3 pens and 3 erasers cost?
  • a)
    Rs. 10
  • b)
    Rs. 15
  • c)
    Rs. 12
  • d)
    Rs. 18
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8...
Let the cost of 1 pencil, 1 pen and 1 eraser be x, y and z respectively.
2x + 4y + 8z = 12      ----(1)
10x + 8y + 4z = 36      ----(2)
Adding (1) and (2), 12x + 12y + 12z = 48
⇒ 3x + 3y + 3z = 48/4 = 12
∴ Cost of 3 pencils, 3 pens and 3 erasers is Rs. 12
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Community Answer
The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8...
To solve this problem, let's assign variables to the cost of each item:
Let the cost of 1 pencil be P.
Let the cost of 1 pen be E.
Let the cost of 1 eraser be R.

Based on the given information, we can form the following equations:
2P + 4E + 8R = 12 (Equation 1)
8P + 10E + 4R = 36 (Equation 2)

To find the cost of 3 pencils, 3 pens, and 3 erasers, we need to multiply each variable by 3:
3P + 3E + 3R = ?

We can solve this system of equations using the method of substitution or elimination.

Using Substitution Method:
Rearrange Equation 1 to solve for P in terms of E and R:
2P = 12 - 4E - 8R
P = 6 - 2E - 4R (Equation 3)

Substitute Equation 3 into Equation 2:
8(6 - 2E - 4R) + 10E + 4R = 36
48 - 16E - 32R + 10E + 4R = 36
-6E - 28R = -12
6E + 28R = 12 (Equation 4)

Multiply Equation 4 by 3 to match the format of the equation we want to find:
18E + 84R = 36 (Equation 5)

Now we have a system of two equations:
3P + 3E + 3R = ?
18E + 84R = 36

Multiply Equation 1 by 3 to match the format of the equation we want to find:
6P + 12E + 24R = 36 (Equation 6)

Subtract Equation 6 from Equation 5:
18E + 84R - (6P + 12E + 24R) = 36 - 36
18E + 84R - 6P - 12E - 24R = 0
6E + 60R - 6P = 0

Divide both sides by 6:
E + 10R - P = 0

Now we can substitute P = 6 - 2E - 4R into the equation above:
E + 10R - (6 - 2E - 4R) = 0
E + 10R - 6 + 2E + 4R = 0
3E + 14R = 6 (Equation 7)

Solve Equations 7 and 5 simultaneously:
3E + 14R = 6
18E + 84R = 36

Multiply Equation 7 by 6:
18E + 84R = 36

Subtract Equation 7 from Equation 5:
18E + 84R - (18E + 84R) = 36 - 6
0 = 30

The result is an inconsistent equation 0 = 30, which means there is no valid solution for this system of equations. However, the options provided do not include "No Solution" as a choice.

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We must ask, what naturalbenefits, like water filtration and animal and(30) plant habitats, are being lost in the construction?Where will the road materials be in a hundredyears, and what will they be doing? What kindsof industries will the road construction andmaintenance support? How will the extra traffic(35) affect air and noise quality, or safety? Is the roadmade of local or imported materials? Are anymaterials being imported from countries withirresponsible labor or environmental practices?Is the contractor chosen through a fair and open(40) bidding process? How might the road surfaceaffect the life span or efficiency of the cars drivingon it? What will be the annual maintenance cost,financially and environmentally?Appreciating opposing viewpoints can lead(45) to important insights. Perhaps nature can doa more efficient and safer job of reusing wastematter than a recycling plant can. Perhaps aneconomic system that accounts for environmentalcosts and benefits will lead to a higher standard(50) of living for the average citizen. Perhaps insertingsome natural resources into a responsible“industrial cycle” is better for the environmentthan conserving those resources. Exploring suchpossibilities openly and respectfully will lead us(55) more reliably to both a healthier economy and ahealthier environment.Passage 2When trying to quantify the costs andbenefits of preserving our natural ecosystems,one difficulty lies in the diffuseness of these(60) effects. Economists have a relatively easy timewith commerce, because money and goods canbe tracked through a series of point-to-pointexchanges. When you pay for something, theexchange of money makes the accounting simple.(65) The diffuse, unchosen costs and benefits thataffect all of us daily—annoying commercials or abeautiful sunset, for instance—are much harderto evaluate.The benefits that ecosystems provide, like(70) biodiversity, the filtration of groundwater, themaintenance of the oxygen and nitrogen cycles,and climate stability, however, are not bought-and-sold commodities. Without them our liveswould deteriorate dramatically, but they are(75) not part of a clear exchange, so they fall into theclass of benefits and costs that economists call“externalities.”The “good feeling” that many people haveabout recycling and maintaining environmental(80) quality is just such an externality. Antienvironmentalists often ridicule such feelingsas unquantifiable, but their value is real: somestock funds only invest in companies with goodenvironmental records, and environmental(85) litigation can have steep costs in terms of moneyand goodwill.Robert Costanza, formerly of the Centerfor Environmental Science at the Universityof Maryland, has attempted to quantify these(90) “external” ecological benefits by tallying thecost to replace natures services. Imagine, forinstance, paving over the Florida Everglades andthen building systems to restore its lost benefits,such as gas conversion and sequestering,(95) food production, water filtration, and weatherregulation. How much would it cost to keep thesesystems running? Not even accounting for someof the most important externalities, like naturalbeauty, the cost would be extraordinarily high.(100) Costanza places it “conservatively” at $33 trilliondollars annually, far more than the economicoutput of all of the countries in the world.Some object to Costanzas cost analysis.Environmentalists argue that we cannot possibly(105) put a price on the smell of heather and a coolbreeze, while industrialists argue that the taskis speculative, unreliable, and an impedimentto economic progress. Nevertheless, Costanzaswork is among the most cited in the fields of(110) environmental science and economics. Forany flaws it might have, his work is giving acommon vocabulary to industrialists andenvironmentalists alike, which we must do ifwe are to coordinate intelligent environmental(115) policy with responsible economic policy.Q.Which choice best exemplifies the “clear exchange” (line 75) mentioned in Passage 2?

Question are based on the following passages and supplementary material.Passage 1 is from F. J. Medina, “How to Talk about Sustainability." ©2015 College Hill Coaching. Passage 2 is adapted from an essay published in 2005 about the economic analysis of environmental decisions.Passage 1Many proponents of recycling assume thatrecycling industrial, domestic, and commercialmaterials does less harm to the environment thandoes extracting new raw materials. Opponents, on(5) the other hand, scrutinize the costs of recycling,arguing that recycling programs often waste moremoney than they save, and that companies canoften produce new products more cheaply thanthey can recycle old ones. The discussion usually(10) devolves into a political battle between theenemies of the economy and the enemies of theenvironment.This demonization serves the debaters(and their fundraisers) but not the debate.(15) Environmentalists are not all ignorant anarchists,and opponents of recycling are not all rapaciousblowhards. For real solutions, we must soberlycompare the many costs and benefits of recyclingwith the many costs and benefits of disposal, as(20) if we are all stewards of both the earth and theeconomy.We must examine the full life cycles ofvarious materials, and the broad effects thesecycles have on both the environment and(25) economy. When debating the cost of a newroad, for instance, it is not enough to simplyconsider the cost of the labor or the provenanceof the materials. We must ask, what naturalbenefits, like water filtration and animal and(30) plant habitats, are being lost in the construction?Where will the road materials be in a hundredyears, and what will they be doing? What kindsof industries will the road construction andmaintenance support? How will the extra traffic(35) affect air and noise quality, or safety? Is the roadmade of local or imported materials? Are anymaterials being imported from countries withirresponsible labor or environmental practices?Is the contractor chosen through a fair and open(40) bidding process? How might the road surfaceaffect the life span or efficiency of the cars drivingon it? What will be the annual maintenance cost,financially and environmentally?Appreciating opposing viewpoints can lead(45) to important insights. Perhaps nature can doa more efficient and safer job of reusing wastematter than a recycling plant can. Perhaps aneconomic system that accounts for environmentalcosts and benefits will lead to a higher standard(50) of living for the average citizen. Perhaps insertingsome natural resources into a responsible“industrial cycle” is better for the environmentthan conserving those resources. Exploring suchpossibilities openly and respectfully will lead us(55) more reliably to both a healthier economy and ahealthier environment.Passage 2When trying to quantify the costs andbenefits of preserving our natural ecosystems,one difficulty lies in the diffuseness of these(60) effects. Economists have a relatively easy timewith commerce, because money and goods canbe tracked through a series of point-to-pointexchanges. When you pay for something, theexchange of money makes the accounting simple.(65) The diffuse, unchosen costs and benefits thataffect all of us daily—annoying commercials or abeautiful sunset, for instance—are much harderto evaluate.The benefits that ecosystems provide, like(70) biodiversity, the filtration of groundwater, themaintenance of the oxygen and nitrogen cycles,and climate stability, however, are not bought-and-sold commodities. Without them our liveswould deteriorate dramatically, but they are(75) not part of a clear exchange, so they fall into theclass of benefits and costs that economists call“externalities.”The “good feeling” that many people haveabout recycling and maintaining environmental(80) quality is just such an externality. Antienvironmentalists often ridicule such feelingsas unquantifiable, but their value is real: somestock funds only invest in companies with goodenvironmental records, and environmental(85) litigation can have steep costs in terms of moneyand goodwill.Robert Costanza, formerly of the Centerfor Environmental Science at the Universityof Maryland, has attempted to quantify these(90) “external” ecological benefits by tallying thecost to replace natures services. Imagine, forinstance, paving over the Florida Everglades andthen building systems to restore its lost benefits,such as gas conversion and sequestering,(95) food production, water filtration, and weatherregulation. How much would it cost to keep thesesystems running? Not even accounting for someof the most important externalities, like naturalbeauty, the cost would be extraordinarily high.(100) Costanza places it “conservatively” at $33 trilliondollars annually, far more than the economicoutput of all of the countries in the world.Some object to Costanzas cost analysis.Environmentalists argue that we cannot possibly(105) put a price on the smell of heather and a coolbreeze, while industrialists argue that the taskis speculative, unreliable, and an impedimentto economic progress. Nevertheless, Costanzaswork is among the most cited in the fields of(110) environmental science and economics. Forany flaws it might have, his work is giving acommon vocabulary to industrialists andenvironmentalists alike, which we must do ifwe are to coordinate intelligent environmental(115) policy with responsible economic policy.Q.The diagram provides information most relevant to

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The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8 pens, 10 pencils and 4 erasers is Rs. 36. How much will 3 pencils, 3 pens and 3 erasers cost?a)Rs. 10b)Rs. 15c)Rs. 12d)Rs. 18Correct answer is option 'C'. Can you explain this answer?
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The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8 pens, 10 pencils and 4 erasers is Rs. 36. How much will 3 pencils, 3 pens and 3 erasers cost?a)Rs. 10b)Rs. 15c)Rs. 12d)Rs. 18Correct answer is option 'C'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8 pens, 10 pencils and 4 erasers is Rs. 36. How much will 3 pencils, 3 pens and 3 erasers cost?a)Rs. 10b)Rs. 15c)Rs. 12d)Rs. 18Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cost of 2 pencil, 4 pens and 8 erasers is Rs. 12 and the cost of 8 pens, 10 pencils and 4 erasers is Rs. 36. How much will 3 pencils, 3 pens and 3 erasers cost?a)Rs. 10b)Rs. 15c)Rs. 12d)Rs. 18Correct answer is option 'C'. Can you explain this answer?.
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