word problem

Question

The difference between two numbers is 27. Three times the smaller is equal to 7 more than the larger. What are the numbers?

Answer 1

Here's what we know:

a - b = 27 (the difference between the two is 27)

3b = a + 7 (three times the smaller is 7 more than the larger)

 

Let's isolate b in the first equation so that we can use the substitution method:

-b = 27 - a

b = a - 27

 

3(a - 27) = a + 7

3a - 81 = a + 7

2a - 81 = a + 7

2a = 88

a = 44

 

b = 44 - 27

b = 17

 

check:

44 - 17 = 27

27 = 27

 

3 * 17 = 44 + 7

51 = 51

Answer 2

x and x+27 are the numbers

3x=x+27+7

3x=x+34

3x-x=34

2x=34

x=17, x+27=44

17 and 44 are the numbers