SOLUTION: Matthew brought $24.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was 1 3 as much as the souvenir, and the souvenir cost 1 2 the cost of th

Question 1158758: Matthew brought $24.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
3
as much as the souvenir, and the souvenir cost
1
2
the cost of the pass. Matthew had $1.50 leftover after buying these items that was the cost of each item?
Found 2 solutions by jim_thompson5910, Boreal:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

p = cost of pass
p/2 = cost of souvenir (which is half the cost of the pass)
p/6 = cost of burger (multiply p/2 by 1/3)
all costs are in dollars

Adding p, p/2, and p/6 leads to
p+(p/2)+(p/6)
(6p/6)+(3p/6)+(p/6)
(6p+3p+p)/6
10p/6
5p/3
This expression represents the total Matthew spent.

We know he started with $24.00 and has $1.50 left over, so he spent 24.00-1.50 = 22.50 dollars. Set this equal to 5p/3 and solve for p

5p/3 = 22.50
5p = 3*22.50 ....... multiply both sides by 3
5p = 67.5
p = 67.5/5 ......... divide both sides by 5
p = 13.50
The pass costs $13.50

Cut this in half to get
p/2 = 13.5/2 = 6.75
The souvenir costs $6.75

Then divide that cost by 3
6.75/3 = 2.25
Or you can plug p = 13.5 into p/6 to get
p/6 = 13.5/6 = 2.25
Either way, the burger costs $2.25

==============================================================
Summary:

Burger cost = $2.25
Souvenir cost = $6.75
Pass cost = $13.50

As a check, those three values should add to $22.50
2.25+6.75+13.50 = 22.50
So our answers are confirmed.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
souvenir is 3x
burger is x
pass is 6x
The total cost of the items was $22.50, after subtracting $1.50 from $24.00
so 10x=$22.50
x=$2.25 for burger
$6.75 for souvenir
$13.50 for pass
Often, it is preferable to make the smallest one x and deal with integers rather than fractions.
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