A theater charges $25 for adults and $15 for children. When the theater increases its prices next year, the price of a child’s ticket will increase to $18 and the cost for the members of a dance club to attend the theater will increase from $450 to $480. Write and solve a system of equations to find how many adults are in the dance club.

Question

04-12-2018
Mathematics

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A theater charges $25 for adults and $15 for children. When the theater increases its prices next year, the price of a child’s ticket will increase to $18 and the cost for the members of a dance club to attend the theater will increase from $450 to $480. Write and solve a system of equations to find how many adults are in the dance club.

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2018-12-13T07:27:19+01:00

Answer: 12 adults are in the dance club.

Step-by-step explanation:

Let x represents the number of adults and y represents the number of children.

Here, theater charges $25 for adults and $15 for children and initially the total charge is $450.

That is, 25x+15y= 450 --------- (1)

Now, he theater increases its prices next year, the price of a child’s ticket will increase to $18 and the cost for the members of a dance club to attend the theater will increase from $450 to $480.

That is, 25x+18y = 480 ----------(2)

Equation(1) - Equation(2)

we get -3y = -30⇒3y = 30⇒y=10

By putting the value of y in equation (1)

25x+15 × 10 = 450 ⇒ 25x = 450 - 150 = 300

⇒25x=300

⇒x = 12

Thus, total number of adult = 12