SOLUTION: Two numbers have the ratio 3 : 4. If 4 is added to each of the numbers the resulting ratio is 4 : 5. The sum of the numbers is SEND ME STEP BY STEP SOLUTION

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Two numbers have the ratio 3 : 4. If 4 is added to each of the numbers the resulting ratio is 4 : 5. The sum of the numbers is SEND ME STEP BY STEP SOLUTION      Log On


   

Question 732496: Two numbers have the ratio 3 : 4. If 4 is added to each of the numbers the resulting ratio is 4 : 5. The sum of the numbers is



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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Two numbers, x and y have the ratio 3+%3A+4.
x%3Ay=3%3A4......eq. 1
If 4 is added to each of the numbers the resulting ratio is 4+%3A+5.
%28x%2B4%29%3A%28y%2B4%29=4%3A5.....eq. 2
solve the system:
x%3Ay=3%3A4......eq. 1
%28x%2B4%29%3A%28y%2B4%29=4%3A5.....eq. 2
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x%3Ay=3%3A4......eq. 1...solve for x

4x=3y
x=3y%2F4.........substitute in eq. 2

%283y%2F4%2B4%29%3A%28y%2B4%29=4%3A5.....eq. 2..solve for y
5%283y%2F4%2B4%29=4%28y%2B4%29

5%28%283y%2B4%2A4%29%2F4%29=4%28y%2B4%29
5%28%283y%2B16%29%2F4%29=4y%2B16
%2815y%2B80%29%2F4=4y%2B16
%2815y%2B80%29=4%2A4y%2B4%2A16
15y%2B80=16y%2B64
15y-15y%2B80=16y-15y%2B64
80=y%2B64

80-64=y%2B64-64
highlight%2816=y%29
go back to x=3y%2F4 and find x
x=3%2A16%2F4
x=3%2Across%2816%294%2Fcross%284%29
x=3%2A4
highlight%28x=12%29

check:
x%3Ay=3%3A4......eq. 1
12%3A16=3%3A4
0.75=0.75
%28x%2B4%29%3A%28y%2B4%29=4%3A5.....eq. 2
%2812%2B4%29%3A%2816%2B4%29=4%3A5
16%3A20=4%3A5
0.8=0.8