Question

7 times a larger number added to 8 times a smaller number totals 44. When 2 times the

smaller number is subtracted from 2 times the larger number, the result is 4. What are the
two numbers?

Answer 1

The two numbers:

4 and 2

Explanation:

7a + 8b = 44 Eq. 1

2a - 2b = 4 Eq. 2

From Eq. 1:

7a = 44 - 8b

a = (44 - 8b) / 7 Eq. 3

From Eq. 2:

2a = 2b + 4

a = (2b+4)/2 Eq. 4

Equalyzing Eq. 3 and Eq. 4:

(44-8b)/7 = (2b+4)/2

2(44-8b) = 7(2b+4)

2*44 + 2*-8b = 7*2b + 7*4

88 - 16b = 14b + 28

88 - 28 = 14b + 16b

60 = 30b

60/30 = b

b = 2

From Eq. 4

a = (2b+4) /2

a = (2*2 + 4) / 2

a = (4+4)/2

a = 4

Check:

From Eq. 1:

7a + 8b = 44

7*4 + 8*2 = 44

28 + 16 = 44