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c) The sum of two numbers is 200. Dividing the first by 12 and the second by 10, the sum of these quotients is 18. What are the numbers?

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Answer to a math question c) The sum of two numbers is 200. Dividing the first by 12 and the second by 10, the sum of these quotients is 18. What are the numbers?

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Tiffany
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103 Answers
x + y = 200
\frac{x}{12} + \frac{y}{10} = 18

To solve:
1. Solve for \( y \) from the first equation and substitute in the second:
y = 200 - x
\frac{x}{12} + \frac{200 - x}{10} = 18

2. Clear the denominators by multiplying through by 60:
5x + 6(200 - x) = 1080
5x + 1200 - 6x = 1080
-x + 1200 = 1080

3. Solve for \( x \):
-x = 1080 - 1200
-x = -120
x = 120

4. Find \( y \):
y = 200 - x
y = 200 - 120
y = 80

Hence, the numbers are:
x = 120, \quad y = 80

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