Samuel wants to buy at least twice as many graphic novels as comic books. Comic books sell for 7 dollars each, and graphic novels sell for 12 dollars each. Samuel can spend a maximum of 50 dollars Let c represent the number of comic books, and let g represent the number of graphic novels. Which system of inequalities can be used to find the number of comic books and graphic novels Samuel can buy?
Answer
A
c plus g is less than or equal to 50 7 c plus 12 g is greater than or equal to 2 c is greater than or equal to 0 g is greater than or equal to 0
B
2 c is less than or equal to g 7 c plus 12 g is less than or equal to 50 c is greater than or equal to 0 g is greater than or equal to 0
C
c plus g is less than or equal to 50 c plus g is greater than or equal to 2 c is greater than or equal to 7 g is greater than or equal to 12
D
c is less than or equal to 2 g 7 c plus 12 g is less than or equal to 50 c is greater than or equal to 0 g is greater than or equal to 0
Explanation
“At least twice as many graphic novels as comic books” means the number of graphic novels, g, is at least 2c, so 2c ≤ g. The total cost is 7c + 12g, and Samuel can spend no more than $50, so 7c + 12g ≤ 50. The quantities must also be nonnegative, giving c ≥ 0 and g ≥ 0. These inequalities are listed in choice C.
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