Mateo and Sydney win a contest. As his prize, Mateo receives $\$ 20$ every hour for one week. As her prize, Sydney receives $\$ 400$ every day for one week. What is the difference in the total amounts of money that they receive over the one week period?
(A) $\$ 560$
(B) $\$ 80$
(C) $\$ 1120$
(D) $\$ 380$
(E) $\$ 784$
Solution 1

Mateo receives $\$ 20$ every hour for one week.

Since there are 24 hours in each day, and 7 days in each week, then Mateo receives $\$ 20 \times 24 \times 7=\$ 3360$ over the one week period.

Sydney receives $\$ 400$ every day for one week.

Since there are 7 days in each week, then Sydney receives $\$ 400 \times 7=\$ 2800$ over the one week period.

The difference in the total amounts of money that they receive over the one week period is $\$ 3360-\$ 2800=\$ 560$.

## Solution 2

Mateo receives $\$ 20$ every hour for one week.

Since there are 24 hours in each day, then Mateo receives $\$ 20 \times 24=\$ 480$ each day.

Sydney receives $\$ 400$ each day, and so Mateo receives $\$ 480-\$ 400=\$ 80$ more than Sydney each day.

Since there are 7 days in one week, then the difference in the total amounts of money that they receive over the one week period is $\$ 80 \times 7=\$ 560$.

ANSWER: (A)