The cost of admission to a popular music concert was $162 for 12 children and 3 adults. The admission was $122 for 8 children and 3 adults in another music concert. How much was the admission for each child and adult?
1 . Understand the problem:
The admission cost for 12 children and 3 adults was $162 .
The admission cost for 8 children and 3 adults was $122 .
2 . Translate the problem to an equation.
Let x represent the admission cost for each child.
Let y represent the admission cost for each adult.
The admission cost for 12 children plus 3 adults is equal to $162 .
That is, 12x+3y=162 .
The admission cost for 8 children plus 3 adults is equal to $122.
That is, 8x+3y=122 .
3 . Carry out the plan and solve the problem.
Subtract the second equation from the first.
12x+3y=162 8x+3y=122−−−−−−−−−−−− 4x = 40 x=10
Substitute 10 for x in 8x+3y=122 .
8(10)+3y=12280+3y=1223y=42y=14
Therefore, the cost of admission for each child is $10 and each adult is $14 .
Answers & Comments
Answer:
Example:
The cost of admission to a popular music concert was $162 for 12 children and 3 adults. The admission was $122 for 8 children and 3 adults in another music concert. How much was the admission for each child and adult?
1 . Understand the problem:
The admission cost for 12 children and 3 adults was $162 .
The admission cost for 8 children and 3 adults was $122 .
2 . Translate the problem to an equation.
Let x represent the admission cost for each child.
Let y represent the admission cost for each adult.
The admission cost for 12 children plus 3 adults is equal to $162 .
That is, 12x+3y=162 .
The admission cost for 8 children plus 3 adults is equal to $122.
That is, 8x+3y=122 .
3 . Carry out the plan and solve the problem.
Subtract the second equation from the first.
12x+3y=162 8x+3y=122−−−−−−−−−−−− 4x = 40 x=10
Substitute 10 for x in 8x+3y=122 .
8(10)+3y=12280+3y=1223y=42y=14
Therefore, the cost of admission for each child is $10 and each adult is $14 .
Step-by-step explanation:
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