SOLUTION: a dance recital had 100 people in the audience. Gina attended with both her parents and found that tickets prices were 50 cents for children, $3 for parents, and $10 for others. If
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Question 1108299: a dance recital had 100 people in the audience. Gina attended with both her parents and found that tickets prices were 50 cents for children, $3 for parents, and $10 for others. If $100 was collected from the 100 people, find out how many parents attended
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Let x be the number of children
Let y be the number of parents
Let z be the number of other people
Note that the statement of the problem requires y to be at least 2, since both Gina's parents attended.
Then...
(1) there were 100 people in attendance
(2) the total cost of the tickets was $100
We have three unknowns but only two equations; but we can find the answer to the problem (or in some similar problems a small family of solutions) using the fact that the variables have whole number values.
To solve this kind of system of equations, we eliminate one variable and use the requirement that the solutions be whole numbers to find the answer.
Double equation (2) and subtract equation (1) from the result:
Solve this equation for one variable in terms of the other:
The only whole number value of y that makes z also a whole number is y=1. That makes z=5; and then x=94, because the total number of people was 100.
But that means there were 94 children, 1 parent, and 5 other people in attendance -- and the problem requires the number of parents to be at least 2.
So THERE IS NO SOLUTION to the problem as stated.
----------------------------------------------------
(response amended...)
Tutor ikleyn is right....
The problem as stated requires that there be at least one child and two parents; but it does not require that there be any other people. So in my equation
y=20 is valid, making z=0 and x=80.
I carelessly read the problem as requiring that there be at least one of each kind of person.
Answer by ikleyn(52805) (Show Source): You can put this solution on YOUR website!
.
One solution still exists:
20 parents and 80 children. (And no other visitors).
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