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svlad2 [7]
3 years ago
14

Jimmy purchased 15 tickets to a concert and spent $140. He purchased some children's tickets and some adult tickets. The childre

n's tickets cost $7 each and the adult tickets cost $12 each. Write a system that represents this situation. How many of each did Jimmy purchase?​
Mathematics
1 answer:
fiasKO [112]3 years ago
4 0

Answer:

Jimmy purchased 8 of the children's ticket and 7 of the adult's ticket.

Step-by-step explanation:

Let c = children tickets

Let a = adult tickets

<u>Given the following data;</u>

Number of tickets = 15

Total amount spent = $140

Cost of each children ticket = $7

Cost of each adult ticket = $12

*Translating the word problem into an algebraic equation (system)*

<em>For the total number of tickets;</em>

c + a = 15 .........equation 1

<em>For the total amount spent;</em>

7c + 12a = 140 ..........equation 2

*Solving the linear equation by using the substitution method*

<em>Making c the subject in equation 1:</em>

c = 15 - a .......equation 3

<em>Substituting "c" into equation 2;</em>

7(15 - a) + 12a = 140

<em>Simplifying the equation, we have;</em>

105 - 7a +12a = 140

105 + 5a = 140

<em>Rearranging the equation, we have;</em>

5a = 140 - 105

5a = 35

a = \frac {35}{5}

a = 5 (For the $12 adult ticket).

To find the number of children tickets;

Substituting "a" into equation 3;

c = 15 - 7

c = 8 (For the $7 children ticket).

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