SOLUTION: the ratio of two integers is 5:3. if the sum of the two integers is no more than 75, find the greatest pair of such integers. i know that n + b is less than or equal to 75, but

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: the ratio of two integers is 5:3. if the sum of the two integers is no more than 75, find the greatest pair of such integers. i know that n + b is less than or equal to 75, but       Log On


   

Question 83359: the ratio of two integers is 5:3. if the sum of the two integers is no more than 75, find the greatest pair of such integers.
i know that n + b is less than or equal to 75, but i forget how to do this kind of problem. thank you so much!
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
The fastest way to do this may very well be to just simply write down a list of all the
integers that will result in exactly a 5 to 3 ratio and see when the total of the two integers
is the maximum it can be without exceeding 75. The pattern for the 5 to 3 ratio is:
.
5:3 total 5+3=8
10:6 total 10+6=16
15:9 total 15+9=24
20:12 total 20+12=32
25:15 total 25+15=40
30:18 total 30+18=48
35:21 total 35+21=56
40:24 total 40+24=64
45:27 total 45+27=72
50:30 total 50+30=80 <--- too big
.
The answer is that the two integers are 45 and 27
.
An interesting pattern is that each step up raises the total by 8. There are 9 steps and
the resulting total is 9 time 8 or 72. So you can just multiply the numerator and the
denominator of 5:3 by 9 and it gets you to 45:27 for a total of 72.
.
Hope this helps you to see your way through the problem.