Question

While shopping at the mall, Tom bought 3 hats and 4 pairs of glasses and spent $123. His friend Jerry bought the same type of items consisting of 1 hat and 3 pairs of glasses and spent $66. How much does a pair of glasses cost? How much does a hat cost?

Answer 1

a pair of glasses costs $17

a hat costs $21

Explanation:

h = hat

g = glasses

3h + 4g = 123

1h + 3g = 66

multiply the 2nd equation by 3

3h + 9g = 198

negate everything in the 1st equation and add it to the 'new' 2nd equation

3h + 9g = 198

+ -3h - 4g = -123

5g = 75

g = 15

substitute the 15 in either one of the 1st equations

1h + 3(15) = 66

h + 45 = 66

h = 66-45

h = 21

to check, substitute both g=15 and h=21 into BOTH 2 original equations.