One number is 5 more than a second number. Three times the first plus twice the second is 30. Find the

Question

 One number is 5 more than a second number. Three times the first plus twice the second is 30. Find the
numbers.

Answer 1

Here's what we know:

a = b + 5 (one number is 5 more than the second)

3a + 2b = 30 (3 times first plus 2 times second is 30)

 

We have a variable value, so plug it in:

3(b + 5) + 2b = 30

3b + 15 + 2b = 30

5b + 15 = 30

Subtract 15:

5b = 15

Divide by 5:

b = 3

 

a = 3 + 5

a = 8

 

Check:

3 * 8 + 2 * 3 = 30

24 + 6 = 30

30 = 30