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Algebra Difficulty 2.8 Junior Find the answer Canada

Exactly 120 tickets were sold for a concert. The tickets cost $12 each for adults,$ 10 each for seniors, and 6 each for children. The number of adult tickets sold was equal to the number of child tickets sold. Given that the total revenue from the ticket sales was 1100, the number of senior tickets sold was

Pick one

Solution

Since the perimeter of the square is $P$ and the 4 sides of a square are equal in length, then each side of the square has length $\frac{1}{4}P$ . We now work backward to determine the width and length of the rectangle.

The width of the rectangle was doubled to produced the side of the square with length $\frac{1}{4}P$ .

Therefore, the width of the rectangle is half of the side length of the square, or $\frac12\times\frac{1}{4}P=\frac{1}{8}P$ .

The length of the rectangle was halved to produce the side of the square with length $\frac{1}{4}P$ .
Therefore, the length of the rectangle is twice the side length of the square, or $2\times\frac{1}{4}P=\frac{1}{2}P$ . Finally, we determine the perimeter of the rectangle having width $\frac{1}{8}P$ and length $\frac{1}{2}P$ , obtaining $2\times\left(\frac{1}{8}P+\frac{1}{2}P\right)=2\times\left(\frac{1}{8}P+\frac{4}{8}P\right)=2\times\left(\frac{5}{8}P\right)=\frac{5}{4}P$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.