The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.

Question

There are two answers in this question. please help!!!

Answer 1

Let a and b be the numbers where a is bigger than b. a-b=44½.

Also, a-7b=7³⁄₁₄. We can write a=b+44½ and substitute in the second equation:

b+44½-7b=7³⁄₁₄. From this 6b=44½-7³⁄₁₄=37+½-³⁄₁₄=37+⁷⁄₁₄-³⁄₁₄=37²⁄₇.

Express the mixed number as an improper fraction: 261/7.

So 6b=261/7, 2b=87/7, b=87/14=6³⁄₁₄. To find a we need to add 44½ to give us 50+³⁄₁₄+⁷⁄₁₄=50⁵⁄₇.

The two numbers are 50⁵⁄₇ and 6³⁄₁₄.