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The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by 3, then all results obtained are equal. What is the difference between the largest and the smallest of the original number?
- a)36
- b)29
- c)21
- d)32
Correct answer is option 'D'. Can you explain this answer?
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The sum of four numbers is 64. If you add 3 to the first number, 3 is...
To solve this problem, let's assign variables to each of the four numbers. Let the first number be x, the second number be y, the third number be z, and the fourth number be w.
According to the given information, we can write the following equations:
Equation 1: x + y + z + w = 64 (The sum of the four numbers is 64)
Equation 2: x + 3 = y - 3 (Adding 3 to the first number is equal to subtracting 3 from the second number)
Equation 3: y - 3 = 3z (Subtracting 3 from the second number is equal to multiplying the third number by 3)
Equation 4: 3z = w/3 (Multiplying the third number by 3 is equal to dividing the fourth number by 3)
We can now solve these equations step by step:
Step 1: From Equation 4, we can rewrite it as w = 9z (by multiplying both sides by 3)
Step 2: Substituting w = 9z into Equation 1, we have x + y + z + 9z = 64
Simplifying this equation, we get:
x + y + 10z = 64 ----(Equation 5)
Step 3: Substituting y = 3z + 3 from Equation 3 into Equation 5, we have:
x + (3z + 3) + 10z = 64
Simplifying this equation, we get:
x + 13z + 3 = 64
x + 13z = 61 ----(Equation 6)
Step 4: Now we have two equations, Equation 6 and Equation 3, with two variables (x and z). We can solve these equations simultaneously to find the values of x and z.
By subtracting Equation 6 from Equation 3, we have:
13z - 3z = 61 - 3
10z = 58
z = 58/10
z = 5.8
Step 5: Substituting the value of z into Equation 6, we have:
x + 13(5.8) = 61
x + 75.4 = 61
x = 61 - 75.4
x = -14.4
Step 6: Now we can find the value of y using Equation 3:
y = 3z + 3
y = 3(5.8) + 3
y = 17.4 + 3
y = 20.4
Step 7: Finally, we can find the value of w using Equation 4:
w = 3z
w = 3(5.8)
w = 17.4
- The largest number is y = 20.4
- The smallest number is x = -14.4
Therefore, the difference between the largest and smallest numbers is:
20.4 - (-14.4) = 20.4 + 14.4 = 34.8
Rounding to the nearest whole number, the difference is 35.
Therefore, the correct answer is option D) 32.
According to the given information, we can write the following equations:
Equation 1: x + y + z + w = 64 (The sum of the four numbers is 64)
Equation 2: x + 3 = y - 3 (Adding 3 to the first number is equal to subtracting 3 from the second number)
Equation 3: y - 3 = 3z (Subtracting 3 from the second number is equal to multiplying the third number by 3)
Equation 4: 3z = w/3 (Multiplying the third number by 3 is equal to dividing the fourth number by 3)
We can now solve these equations step by step:
Step 1: From Equation 4, we can rewrite it as w = 9z (by multiplying both sides by 3)
Step 2: Substituting w = 9z into Equation 1, we have x + y + z + 9z = 64
Simplifying this equation, we get:
x + y + 10z = 64 ----(Equation 5)
Step 3: Substituting y = 3z + 3 from Equation 3 into Equation 5, we have:
x + (3z + 3) + 10z = 64
Simplifying this equation, we get:
x + 13z + 3 = 64
x + 13z = 61 ----(Equation 6)
Step 4: Now we have two equations, Equation 6 and Equation 3, with two variables (x and z). We can solve these equations simultaneously to find the values of x and z.
By subtracting Equation 6 from Equation 3, we have:
13z - 3z = 61 - 3
10z = 58
z = 58/10
z = 5.8
Step 5: Substituting the value of z into Equation 6, we have:
x + 13(5.8) = 61
x + 75.4 = 61
x = 61 - 75.4
x = -14.4
Step 6: Now we can find the value of y using Equation 3:
y = 3z + 3
y = 3(5.8) + 3
y = 17.4 + 3
y = 20.4
Step 7: Finally, we can find the value of w using Equation 4:
w = 3z
w = 3(5.8)
w = 17.4
- The largest number is y = 20.4
- The smallest number is x = -14.4
Therefore, the difference between the largest and smallest numbers is:
20.4 - (-14.4) = 20.4 + 14.4 = 34.8
Rounding to the nearest whole number, the difference is 35.
Therefore, the correct answer is option D) 32.
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The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by 3, then all results obtained are equal. What is the difference between the largest and the smallest of the original number?a)36b)29c)21d)32Correct answer is option 'D'. Can you explain this answer?
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