Question

Four subtracted from four times the smaller is equal to the larger number. Twice the larger number equals six times the smaller number. What are the numbers?

Answer 1

the answer is four and twelve

Answer 2

12 and 4

Explanation:

We could set up two equations with the given information.

Let a be the larger number, and b be the smaller number.

4b - 4 = a (Four subtracted from four times the smaller is equal to the larger number.)

2a = 6b (Twice the larger number equals six times the smaller number.)

With the 1st equation, we could substitute a = 4b - 4 into the second equation.

We get

2(4b-4) = 6b

8b - 8 = 6b

2b = 8

b = 4

Substituting back into the first equation,

a = 4(4) - 4 = 12

Therefore the two numbers are 12 and 4.