Chapter 5: Q. 243 (page 658)

In the following exercises, translate to a system of equations and solve.
Tickets for a dance recital cost $15 for adults and $7 for children. The dance company sold 253 tickets and the total receipts were $2,771. How many adult tickets and how many child tickets were sold?

Short Answer

Expert verified

The number of children tickets are 128 and number of adult tickets are 125.

Step by step solution

Step 1. Given Information

The given data is that Tickets for a dance recital cost $15 for adults and $7 for children. The dance company sold 253 tickets and the total receipts were $2,771.

Step 2. Calculation

Let x be the number of children tickets and ybe the number of adult tickets.

Total number of tickets is 253 that is $x + y = 253 - - (1)$

The total receipts were $2771 that can be expressed as $15 x + 7 y = 2771 - - (2)$

Multiply equation (1) with 7 and write the revised equation.

$7 (x + y) = 7 (253) 7 x + 7 y = 1771 - - (3)$

Solve the equations (2) and (3) by subtracting equation (3) from equation (2) to find the value of x.

$15 x + 7 y - 7 x - 7 y = 2771 - 1771 8 x = 1000 x = 125$

Substitute the value of x in equation (1) to find the value of y.

$125 + y = 253 y = 253 - 125 y = 128$

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In the following exercises, translate to a system of equations and solve.
Tickets for a dance recital cost \(15 for adults and \)7 for children. The dance company sold 253 tickets and the total receipts were $2,771. How many adult tickets and how many child tickets were sold?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

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In the following exercises, translate to a system of equations and solve. Tickets for a dance recital cost \(15 for adults and \)7 for children. The dance company sold 253 tickets and the total receipts were $2,771. How many adult tickets and how many child tickets were sold?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, translate to a system of equations and solve.
Tickets for a dance recital cost \(15 for adults and \)7 for children. The dance company sold 253 tickets and the total receipts were $2,771. How many adult tickets and how many child tickets were sold?