47 adult tickets and 37 children ticket were sold in the show because when you multiply 47 by $105 and 37 by $60 and add them the answers is $7155
Step-by-step explanation:
A local dinner theater sells adult tickets and children tickets
- The adult ticket costs $105 each
- The children ticket costs $60 each
- For a certain show the theater sells 84 tickets for a total of $7155
We need to find how many tickets of each type were sold
Assume that x adult tickets and y children tickets were sold
∵ The number of adult tickets sold is x
∵ The number of children tickets sold is y
∵ The theater sold 84 tickets in a certain show
- Add x and y , then equate the sum by 84
∴ x + y = 84 ⇒ (1)
∵ The adult ticket costs $105
∵ The children ticket costs $60
∵ The total money of the tickets is $7155
- Multiply x by 105, and y by 60, then add the products and
equate the sum by 7155
∴ 105x + 60y = 7155 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -60 to eliminate y
∴ -60x - 60y = -5040 ⇒ (3)
- Add equations (2) and (3)
∴ 45x = 2115
- Divide both sides by 45
∴ x = 47
- Substitute the value of x by 47 in equation (1) to find y
∵ 47 + y = 84
- Subtract 47 from both sides
∴ y = 37
47 adult tickets and 37 children ticket were sold in the show
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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