Tickets 7

Tickets to a concert cost $2 for children, $3 for teenagers, and $5 for adults. When 570 people attended the concert, the total ticket receipts were $1950. Compared to the number of children in attendance, three-fourths as many teenagers attended. How many teenagers attended?

Correct answer:

t =  150

Step-by-step explanation:

$$\begin{gathered} 2c+3t+5a=1950 \\ c+t+a=570 \\ t=\frac{3}{4}\cdot c \\ 2\cdot c+3\cdot t+5\cdot a=1950 \\ c+t+a=570 \\ t=3/4\cdot c \\ 5a+2c+3t=1950 \\ a+c+t=570 \\ 3c-4t=0 \\ Row2-\frac{1}{5}\cdot Row1\to Row2 \\ 5a+2c+3t=1950 \\ 0.6c+0.4t=180 \\ 3c-4t=0 \\ Pivot:Row2\leftrightarrow Row3 \\ 5a+2c+3t=1950 \\ 3c-4t=0 \\ 0.6c+0.4t=180 \\ Row3-\frac{0.6}{3}\cdot Row2\to Row3 \\ 5a+2c+3t=1950 \\ 3c-4t=0 \\ 1.2t=180 \\ t=\frac{180}{1.2}=150 \\ c=\frac{0+4t}{3}=\frac{0+4\cdot 150}{3}=200 \\ a=\frac{1950-2c-3t}{5}=\frac{1950-2\cdot 200-3\cdot 150}{5}=220 \\ a=220 \\ c=200 \\ t=150 \end{gathered}$$

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