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A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will be
- a)18
- b)22
- c)26
- d)30
- e)34
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
A tea shop offers tea in cups of three different sizes. The product of...
Let's rephrase the given information and calculations:
Assuming we have three cup sizes: Small, Medium, and Large, Let the price of a Small cup be 2x. Let the price of a Medium cup be 5x. Let the price of a Large cup be Ax.
According to the given information, The product of the prices (2x * 5x * Ax) equals 800.
After a price increase, The new product of the prices ((2x + 6) * (5x + 6) * Ax) equals 3200.
By dividing both of these equations, we find: (10x2 + 42x + 36) / (40x2) = 1.
Simplifying the equation gives us: 30x2 - 42x - 36 = 0.
Further simplification leads to: 5x2 - 7x - 6 = 0.
Factoring the equation, we get: (5x + 3)(x - 2) = 0.
Therefore, x = 2.
Now, we can determine the prices for each cup size: Small cup price = 4. Medium cup price = 10. Large cup price = 20 (as the product is 800).
To find the sum of the original unit prices, we add: Small price + Medium price + Large price = 4 + 10 + 20 = 34.
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Community Answer
A tea shop offers tea in cups of three different sizes. The product of...
Let's assume the prices of the smallest, medium, and largest sizes of tea cups are x, y, and z dollars respectively.
Given that the product of the prices of the three sizes is equal to 800, we have the equation:
x * y * z = 800
We are also given that the prices of the smallest and medium sizes are in the ratio 2:5. We can express this as:
x/y = 2/5
Simplifying the ratio, we get:
5x = 2y
We are further given that when the prices of the smallest and medium sizes are increased by $6 and the price of the largest size remains unchanged, the product of the prices becomes 3200. We can set up the following equation:
(x + 6) * (y + 6) * z = 3200
Now, let's solve these equations to find the values of x, y, and z.
Solution:
1. Use the ratio to express y in terms of x:
5x = 2y
y = (5/2)x
2. Substitute the value of y in the product equation:
x * (5/2)x * z = 800
(5/2)x^2 * z = 800
(5/2)(x^2) * z = 800
(5/2)(x^2) * z = 2^5 * 5^2
3. Simplify the equation:
(5/2)(x^2) * z = 2^5 * 5^2
(5/2)(x^2) * z = 32 * 25
(5/2)(x^2) * z = 800
4. Divide both sides of the equation by (5/2):
x^2 * z = 800 / (5/2)
x^2 * z = 800 * (2/5)
x^2 * z = 320
5. Now, let's substitute the value of z in terms of x:
z = 320 / x^2
6. Substitute the value of z in the equation (x + 6) * (y + 6) * z = 3200:
(x + 6) * (y + 6) * (320 / x^2) = 3200
7. Simplify the equation:
(x + 6) * (y + 6) * (320 / x^2) = 3200
(x + 6) * (y + 6) = 3200 * (x^2 / 320)
(x + 6) * (y + 6) = x^2
8. Expand the equation:
xy + 6y + 6x + 36 = x^2
9. Rearrange the equation:
x^2 - xy - 6y - 6x - 36 = 0
10. Now, let's solve this quadratic equation to find the values of x and y.
We can either factorize or use the quadratic formula:
x^2 - xy - 6y - 6x - 36 = 0
(x - 6)(x + y - 6) - 36 = 0
(x + y - 6)(x - 6) =
Given that the product of the prices of the three sizes is equal to 800, we have the equation:
x * y * z = 800
We are also given that the prices of the smallest and medium sizes are in the ratio 2:5. We can express this as:
x/y = 2/5
Simplifying the ratio, we get:
5x = 2y
We are further given that when the prices of the smallest and medium sizes are increased by $6 and the price of the largest size remains unchanged, the product of the prices becomes 3200. We can set up the following equation:
(x + 6) * (y + 6) * z = 3200
Now, let's solve these equations to find the values of x, y, and z.
Solution:
1. Use the ratio to express y in terms of x:
5x = 2y
y = (5/2)x
2. Substitute the value of y in the product equation:
x * (5/2)x * z = 800
(5/2)x^2 * z = 800
(5/2)(x^2) * z = 800
(5/2)(x^2) * z = 2^5 * 5^2
3. Simplify the equation:
(5/2)(x^2) * z = 2^5 * 5^2
(5/2)(x^2) * z = 32 * 25
(5/2)(x^2) * z = 800
4. Divide both sides of the equation by (5/2):
x^2 * z = 800 / (5/2)
x^2 * z = 800 * (2/5)
x^2 * z = 320
5. Now, let's substitute the value of z in terms of x:
z = 320 / x^2
6. Substitute the value of z in the equation (x + 6) * (y + 6) * z = 3200:
(x + 6) * (y + 6) * (320 / x^2) = 3200
7. Simplify the equation:
(x + 6) * (y + 6) * (320 / x^2) = 3200
(x + 6) * (y + 6) = 3200 * (x^2 / 320)
(x + 6) * (y + 6) = x^2
8. Expand the equation:
xy + 6y + 6x + 36 = x^2
9. Rearrange the equation:
x^2 - xy - 6y - 6x - 36 = 0
10. Now, let's solve this quadratic equation to find the values of x and y.
We can either factorize or use the quadratic formula:
x^2 - xy - 6y - 6x - 36 = 0
(x - 6)(x + y - 6) - 36 = 0
(x + y - 6)(x - 6) =
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Question Description
A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer?.
A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer?.
Solutions for A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer?, a detailed solution for A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of A tea shop offers tea in cups of three different sizes. The product of the prices (in $) of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by $ 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes (in $) will bea)18b)22c)26d)30e)34Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
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