lheiannie07 wrote:Alex paid a $12 fee to receive a 10% discount off of the list price on all books he bought in a six-month period. Victor paid a $15 fee to receive a 15% discount off of the list price on all books he bought in the same period. If each bought books with a total list price of b during that period and each paid the same net amount, including the discount and the fee, what is b ?
A. $54
B. $60
C. $66
D. $100
E. $120
We can PLUG IN THE ANSWERS, which represent the list price.
When the correct answer is plugged in, Alex and Victor pay the same amount.
B: 60
Since Alex receives a 10% discount for a $12 fee, the amount paid by Alex = 60 - (10% of 60) + ($12 fee) = 60-6+12 = 66.
Since Victor receives a 15% discount for a $15 fee, the amount paid by Victor = 60 - (15% of 60) + ($15 fee) = 60-9+15 = 66.
Success!
The correct answer is
B.
Algebra:
Since Alex receives a 10% discount for a $12 fee, he pays 90% of the list price plus a $12 fee:
(90/100)b + 12.
Since Victor receives a 15% discount for a $15 fee, he pays 85% of the list price plus a $15 fee:
(85/100)b + 15.
Since each pays the same amount, the expressions in blue are equal:
(90/100)b + 12 = (85/100)b + 15
90b + 1200 = 85b + 1500
5b = 300
b = 60.
More importantly:
Why didn't Alex and Victor just pay the list price?
At $60, it is less than the amount each paid ($66).
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