Question

The sum of two numbers is 30. If we double the larger number, and subtract three times the smaller number, the result is 5. What is the positive difference between the two numbers?

Answer 1

Answer: The difference is 8.

Explanation:

We will let l represent the larger number s represent the smaller number.

so we know that L + S =30

Also 2L - 3S = 5 shows the relationship between the numbers.

Now we have two equations.

L + S =30

2L - 3S = 5 solve using any method.

L + S =30 solve for L and substitute it into the second equation.

L + S = 30

-S -S

L = 30 -S

2(30-s) - 3s = 5 Distribute

60 - 2s - 3s = 5 combine like terms

60 -5s = 5

-60 -60

-5s = -55

s = 11

We know the smaller number is 11 so to find the larger number we will subtract 11 from 30.

30 -11 = 19

The larger number is 19

so To find the difference we will subtract 11 from 19.

19 -11 = 8

Answer 2

8 is the difference, and 19 and 11 are the numbers. Hope this helped!