a company that provides whale - watching tours takes groups of 21 people at a time. the companys revenue is…
a company that provides whale - watching tours takes groups of 21 people at a time. the companys revenue is 80 dollars per adult and 60 dollars per child. if the companys revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?\na 3\nb 9\nc 12\nd 18
Answer
Explanation:
Step1: Let number of adults be $x$ and children be $y$.
We know $x + y=21$ (total number of people in the group) and revenue equation: $80x + 60y=1440$.
Step2: Express $x$ in terms of $y$ from first - equation.
$x = 21 - y$.
Step3: Substitute $x$ into the revenue equation.
$80(21 - y)+60y = 1440$. Expand: $1680-80y + 60y=1440$. Combine like - terms: $1680-(80y - 60y)=1440$, so $1680 - 20y=1440$.
Step4: Solve for $y$.
Subtract 1680 from both sides: $-20y=1440 - 1680=-240$. Divide both sides by - 20: $y=\frac{-240}{-20}=12$. Then find $x$: $x = 21 - 12 = 9$. The total number of people in the group is 21.