Peter delivered 210 food orders in a week. For every order that was delivered on time, he earned $3.50. For every order that was delivered late, he would not earn any money and would have to pay a fine of $4.30 instead. He received $532.20 at the end of the week. How many orders were delivered on time?
Let the number of orders that were delivered on time be a.
3.5a−4.3(210−a)=532.2
3.5a−903+4.3a=532.2
7.8a−903=532.2
7.8a=1435.2
a=184
Now we should check our answers:
If 184 orders were delivered on time, Peter would have
184×$3.5=$644.
If there were 184 orders that were on time, there were
210−184=26 late orders.
We should now subtract
26×$4.3=$111.8
from Peter's $644.
$644−$111.8=$532.2
184 orders were delivered on time.