SOLUTION: Hi Jerry wendy and Alice were given some tickets to sell. Each one sold for $5. Jerry sold 3/7 of the tickets. Wendy sold 1/3 of what Alice sold. If wendy sold 60 fewer tickets th

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Question 1185841: Hi
Jerry wendy and Alice were given some tickets to sell. Each one sold for $5. Jerry sold 3/7 of the tickets. Wendy sold 1/3 of what Alice sold. If wendy sold 60 fewer tickets than Jerry, how much money did they collect.
My son had difficulty with this question since we are not told what fraction of the tickets Alice sold
Thanks

Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Ticket price is for later in the solution; not sooner. 
Jerry           (3/7)T
Wendy           (3/7)T-60
Alice


Jerry and Wendy were easier to assign than how many Alice sold.

"Wendy sold 1/3 of what Alice sold."
This means that Alice sold three times as much as did Wendy. 
Jerry           (3/7)T
Wendy           (3/7)T-60
Alice           3((3/7)T-60)
TOTAL           T

%283%2F7%29T%2B%283%2F7%29T-60%2B3%28%283%2F7%29T-60%29=T-------------This should give how many tickets total were sold.

%286%2F7%29T-60%2B9T%2F7-180=T
15T%2F7-240=T
8T%2F7=240
T%2F7=30
highlight_green%28T=210%29-------number of tickets

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor uses x for the total number of tickets, resulting in a rather complicated equation that needs to be solved to find the solution.

That's fine; but taking a bit of time to figure out a way to set up the problem that make solving it easier is well worthwhile.

Given that Jerry sold 3/7 of the tickets, here is how I would set up and solve the problem.

Let the total number of tickets sold be 7x
Then the number Jerry sold was 3x
So the total that Wendy and Alice sold was 7x-3x=4x

Then, since Wendy sold 1/3 as many as Alice, and together they sold 4/7 of them...

3x = number Alice sold
x = number Wendy sold

So the number Jerry sold was 3x, and the number Wendy sold was x, and the difference between those two numbers was 60:

3x-x=60
2x=60
x=60/2=30

Numbers of tickets sold:
Jerry: 3x=90
Alice: 3x=90
Wendy: x=30
total: 210

The tickets cost $5 each; how much money did they collect?

ANSWER: 210($5) = $1050

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Hi
Jerry wendy and Alice were given some tickets to sell. Each one sold for $5. Jerry sold 3/7 of the tickets. Wendy sold 1/3 of what Alice sold. If wendy sold 60 fewer tickets than Jerry, how much money did they collect.
My son had difficulty with this question since we are not told what fraction of the tickets Alice sold
Thanks 
Let multiplicative factor for number of tickets sold be x
Then Jerry sold 3x, while Alice and Wendy sold a total of 4x tickets
Wendy sold 1%2F3 of what Alice sold, or Alice sold 3 times what Wendy sold, or 3W, with W being the number Wendy sold
We then get: W + 3W = 4x_____4W = 4x____matrix%281%2C5%2C+W%2C+%22=%22%2C+4x%2F4%2C+%22=%22%2C+x%29

Since Wendy sold 60 FEWER tickets than Jerry, we then get: x = 3x  -  60
x - 3x = - 60
  - 2x = - 60
Multiplicative factor/Number Wendy sold, or matrix%281%2C5%2C+x%2C+%22=%22%2C+%28-+60%29%2F%28-+2%29%2C+%22=%22%2C+30%29

Number Jerry sold: 3x = 3(30) = 90
Number Alice sold: 3W = 3x = 3(30) = 90
Number all 3 sold: 30 + 2(90) = 210

Since the 3 sold a total of 210 tickets, the amount they collected = highlight_green%28matrix%281%2C3%2C+210%285%29%2C+%22=%22%2C+%22%241%2C050%22%29%29