SOLUTION: I know the answer from the answer book, but I can't figure out how to set up the problem to arrive at the answer. So I'd like to see an example of how to set up the problem. Here i

Question 122282: I know the answer from the answer book, but I can't figure out how to set up the problem to arrive at the answer. So I'd like to see an example of how to set up the problem. Here is the problem:
The ratio of the two numbers was 7 to 2. When Sir Richard and Marion multiplied the denominator by 10 they found that the result was 84 greater than twice the numerator. What were the numbers?
Thanks
Answer by ankor@dixie-net.com(15622) (Show Source):
You can put this solution on YOUR website!
The ratio of the two numbers was 7 to 2. When Sir Richard and Marion multiplied the denominator by 10 they found that the result was 84 greater than twice the numerator. What were the numbers?
:
Here's one way that should make sense to you:
Let x = the numerator
Let y = the denominator
:
It says,"The ratio of the two numbers was 7 to 2." so we can say:
=
Cross multiply and get x in terms of y
2x = 7y
x = y
x = 3.5y
:
Write an equation for the statement:
" multiplied the denominator by 10 they found that the result was 84 greater than twice the numerator."
10y = 2x + 84
:
Substitute 3.5y for x
10y = 2(3.5y) + 84
10y = 7y + 84
10y - 7y = 84
3y = 84
y =
y = 28 is the denominator
:
Find x:
We know x = 3.5y, therefore:
x = 3.5(28)
x = 98 is the numerator
:
Check solution by reducing the fraction:
=