HARD Math question from recent SAT with my solution
A certain book is available from a publishing company in both hardcover and paperback. The table shows the revenue and cost in 2016 for each of the hardcover and paperback books produced by the company.
Hardcover Paperback
Revenue $24 $18
Cost $14 $10
In 2016 the total cost for 200 of the books that were sold was between $2,200 and $2,400. Which of the following could be the number of hardcover books that were sold?
A. 80
B. 120
C. 160
D. 200
The total Hardcover and Paperback were 200 so
H+P=200
P=200-H
The total cost of both were between 2200 and 2400 so
2200<14H+10P<2400
Substitution
2200<14H+10(200-H)<2400
2200<14H+2000-10H<2400
200<4H<400
50<H<100
So 80 fits