Let's write an inequality that describes Craig's desired earnings. The phrase at least is equivalent to saying greater than or equal to, which algebraically can be written as

\geq .

Therefore, we can describe Craig's desired earnings.

Earnings \geq 600

Next, let's find how much money Craig earns in a week by working

40

hours. The pay rate is

$ 12.80

per hour so we can find the total weekly earnings multiplying this rate by

40

hours.

40 \cdot 12.80 = 512

Craig can earn

$ 512

in a week by working

40

hours but this is not enough to reach Craig's earnings goal, so he needs to put in overtime. We know that Craig is paid

$ 19.20

per hour of overtime. So, if the extra number of hours Craig needs to put in to earn at least

$ 600

is

x,

we can rewrite the left-hand side of our inequality with the expression

19.20 x .

512 + 19.20 x \geq 600

By solving this inequality for

x

we can determine the number of hours Craig has to put in.

512 + 19.20 x \geq 600

SubIneq

$LHS - 512 \geq RHS - 512$

19.20 x \geq 88

DivIneq

$LHS / 19.20 \geq RHS / 19.20$

h = 4.853333 \dots

We are only given whole hours as options, and since Craig wants to earn at least

$ 600

we have to round up the number of extra hours Craig has to put in to

5

hours. In total Craig has to put in

45

hours, which corresponds to option H.

Exercise