Question

Ethan is thinking of two numbers. The difference of two numbers is 5. Five times the lesser number minus the greater number is 7. What are Ethan's numbers.

Answer 1

If we write the bigger number as x, and the smaller number as y, we can write it as simultaneous equations.

So, if the difference is 5, we can say that

x-y=5

And if five times the smaller number minus the greater number is 7, then we can write that as

5y-x=7

You can add these together to get 4y=12, and if we simplify, we get y=3.

We know that the difference is 5, so 3+5=8.

Therefore, Ethan's numbers are 3 and 8.