One number is 8 times another number. The numbers are both positive and have a difference of 70. Find the numbers. Which of the following equations could be used to solve the problem? 8 x - x = 70

Question

One number is 8 times another number. The numbers are both positive and have a difference of 70. Find the numbers.

Which of the following equations could be used to solve the problem?

8 x - x = 70

x - 8 x = 70

x - 8 = 70

Answer 1

8x - x = 70 ⇒

7x = 70

x = 10

8x = 8(10) = 80

Test the answer.

Answer 2

"One number is 8 times another number." Right there we can remove the third possible answer as that doesn't have 8x, but just 8.

"Both numbers are positive" Noted. Stick a pin in that.

"They have a difference of 70." So we're subtracting here. x needs to be positive (as we were told above), and 70 is positive. This means that the coefficient caused by the subraction also needs to be positive because if it turned negative, it would turn x negative as well. That means we need the lager number minus the smaller number, or:

8x - x = 70

If we had x - 8x = 70, then once we subtracted we would have:

-7x = 70

Dividing by -7, we would then have:

x = -10, which is not positive, but negative, and therefore not a possible equation.