Question

The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k?\

Answer 1

Hlw mate!!


The ratio of two positive numbers is 3 to 4 --> ab=3x4xab=3x4x, for some positive integer xx.

If k is added to each number the new ratio will be 4 to 5 --> 3x+k4x+k=453x+k4x+k=45 --> 15x+5k=16x+4k15x+5k=16x+4k --> x=kx=k.

The sum of the numbers will be 117 (I believe it means that the sum of the numbers after we add k to each) --> 3x+k+4x+k=1173x+k+4x+k=117 --> 7x+2k=1177x+2k=117 --> as from above x=kx=k --> 7k+2k=1177k+2k=117 --> k=13k=13.


Hope it helpful