The larger of two numbers is seven more than five times the smaller. If their sum is 61, what are the numbers?
Question
The larger of two numbers is seven more than five times the smaller. If their sum is 61, what are the numbers?
Solution
Let's denote the smaller number as x and the larger number as y.
From the problem, we have two equations:
-
y = 5x + 7 (since the larger number is seven more than five times the smaller number)
-
x + y = 61 (since their sum is 61)
We can substitute equation 1 into equation 2 to solve for x:
x + 5x + 7 = 61 6x + 7 = 61 6x = 61 - 7 6x = 54 x = 54 / 6 x = 9
Substitute x = 9 into equation 1 to solve for y:
y = 5*9 + 7 y = 45 + 7 y = 52
So, the smaller number is 9 and the larger number is 52.
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