SOLUTION: Two numbers are in a ratio of 7 to 10. If 24 is added to each number, the resulting numbers are in the ratio of 1 to 2. Find the smaller of the two original numbers.

Algebra ->  Equations -> SOLUTION: Two numbers are in a ratio of 7 to 10. If 24 is added to each number, the resulting numbers are in the ratio of 1 to 2. Find the smaller of the two original numbers.      Log On


   

Question 73709: Two numbers are in a ratio of 7 to 10. If 24 is added to each number, the resulting numbers are in the ratio of 1 to 2. Find the smaller of the two original numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers are in a ratio of 7 to 10. If 24 is added to each number, the resulting numbers are in the ratio of 1 to 2. Find the smaller of the two original numbers.
:
Let x be the multiplier of the two numbers:
:
%28%287x%2B24%29%29%2F%28%2810x%2B24%29%29 = 1%2F2
:
Cross multiply and you have:
2(7x+24) = 10x + 24
14x + 48 = 10x + 24
14x - 10x = 24 - 48
4x = -24
x = -24/4
x = -6
:
:
We have:
%28%287%28-6%29%2B24%29%29%2F%28%2810%28-6%29%2B24%29%29 = 1%2F2
:
%28%28-42%2B24%29%29%2F%28%28-60%2B24%29%29 = 1%2F2
:
%28%28-18%29%29%2F%28%28-36%29%29 = 1%2F2; A minus over a minus is a +
:
Let you decide which is the smaller of the two numbers