A number, x, is 4 times another number, y. The difference between the two numbers is 18. What is the value of the larger number?

Question

A number, x, is 4 times another number, y. The difference between the two numbers is 18. What is the value of the larger number?

Answer 1

I like to always put everything in terms of one variable from the start. So, start by saying “let x = the first number” (which in the word problem is y). The other number is 4 times x. Then, the difference between the two numbers is 4x-x=18. Subtract x from 4x gives 3x. Then divide each side by 3 which results in x=6. This is the first number. The other number is 4 times x = 4*6=24. So the larger number is 24. It’s always good to double check and make sure the answer makes sense. Certainly 24-6 =18. So the difference in the two numbers is 18. The other part to check is that one number is 4 times the other. 24 is 4 times 6. So we confirmed that the larger number is indeed 24.

Answer 2

if x = 4 * y and x - y = 18 then you can simply substitute the value of x into the second equation and solve for Y.

(4 * y) - y = 18 gives you 3 * y = 18 then divide by 3 on each side and you see that y = 6 and therefore x = 12