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A theater sold 300 tickets to a special benefit performance. The ticket prices were
$4 for children and
$6 for adults. If three times as many adults attended as children, how many adults attended?

$4$ . A theater sold $300$ tickets to a special benefit performance. The ticket prices were $\$ 4$ for children and $\$ 6$ for adults. If three times as many adults attended as children, how many adults attended?

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Identify quotients of rational numbers: word problems

Full solution

Q.

4

. A theater sold

300

tickets to a special benefit performance. The ticket prices were

\$ 4

for children and

\$ 6

for adults. If three times as many adults attended as children, how many adults attended?

Denote numbers of attendees: Let's denote the number of children as $C$ and the number of adults as $A$ . According to the problem, three times as many adults attended as children, so we can write the relationship as $A = 3C$ .
Total tickets sold: We also know that the total number of tickets sold was $300$ . This gives us the equation $C + A = 300$ .
Substitute relationship into equation: Substituting the relationship from the first step into the second equation, we get $C + 3C = 300$ , which simplifies to $4C = 300$ .
Solve for number of children: Now we solve for $C$ by dividing both sides of the equation by $4$ : $\frac{4C}{4} = \frac{300}{4}$ , which gives us $C = 75$ . This means $75$ children attended the performance.
Find number of adults: Since $A = 3C$ , we can now find the number of adults by multiplying the number of children by $3$ : $A = 3 \times 75 = 225$ .

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