Question

the ratio of two numbers is 5/4 and the first number is 7 more than the second number. to determine each of these numbers, let x be the first number. Since the first number is 7 more than the second number, and since the first number is x, what is the second number?

Answer 1

the first number is 35 and the second number is 28.
You can get all complicated with this by using the Cramer's rule, or you can try this trick.
the ratio is 5/4 and x is 7 more than y, therefore 5 in 5/4 is x because x is the bigger number thus has a bigger portion.
5 x 7=35, which is x
35-7=28, which is y

Answer 2

If the first number is x and it is 7 more than the second number, the second number is equal to x - 7. Given that their ratio is 5/4. The equation that represents this situation is,
x / (x - 7) = 5/4
The value of x is 35 and the second number is 28.