A company that provides whale-watching tours takes groups of 21 people at a time. The company’s revenue is 80 dollars

Question

A company that provides whale-watching tours takes groups of $21$ people at a time. The company’s revenue is $80$ dollars per adult and $60$ dollars per child. If the company’s revenue for one group consisting of adults and children was $1,440$ dollars, how many people in the group were children?

A.

$3$

B.

$9$

C.

$12$

D.

$18$

Accepted Answer

Choice C is correct. Let x represent the number of children in a whale-watching tour group. Let y represent the number of adults in this group. Because it's given that 21 people are in a group and the group consists of adults and children, it must be true that x + y = 21 . Since the company's revenue is 60 dollars per child, the total revenue from x children in this group was 60 x dollars. Since the company's revenue is 80 dollars per adult, the total revenue from y adults in this group was 80 y dollars. Because it's given that the total revenue for this group was 1,440 dollars, it must be true that 60 x + 80 y = 1,440 . The equations x + y = 21 and 60 x + 80 y = 1,440 form a linear system of equations that can be solved to find the value of x , which represents the number of children in the group, using the elimination method. Multiplying both sides of the equation x + y = 21 by 80 yields 80 x + 80 y = 1,680 . Subtracting 60 x + 80 y = 1,440 from 80 x + 80 y = 1,680 yields ( 80 x + 80 y ) - ( 60 x + 80 y ) = 1,680 - 1,440 , which is equivalent to 80 x - 60 x + 80 y - 80 y = 240 , or 20 x = 240 . Dividing both sides of this equation by 20 yields x = 12 . Therefore, 12 people in the group were children. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect. This is the number of adults in the group, not the number of children in the group. Choice D is incorrect and may result from conceptual or calculation errors.

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