Question

A large employer gives each new hire an aptitude test, which is scored from 1 to 20. Let T be a worker's score on the test. The firm then pays the new worker a wage of w = 0.6T + 0.4G where G is the average test score for the worker's gender-16 for women; 12 for men. How much more is a woman paid than a man when both scored a 10 on the test?

Answer 1

A woman paid 1.6 more than a man when both scored a 10 on the test.

Explanation:

Let T be a worker's score on the test.

The firm then pays the new worker a wage of

`w=0.6T+0.4G`

where G is the average test score for the worker's gender 16 for women; 12 for men.

We need to find how much more is a woman paid than a man when both scored a 10 on the test.

The wage of a woman who scored 10 on the test is

`w_1=0.6(10)+0.4(16)`

`w_1=6.0+6.4=12.4`

The wage of a man who scored 10 on the test is

`w_2=0.6(10)+0.4(12)`

`w_2=6.0+4.8=10.8`

The difference between wages is

`w_1-w_2=12.4-10.8=1.6`

Therefore a woman paid 1.6 more than a man when both scored a 10 on the test.