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Question 1189424: A bleacher ticket for the high school baseball game costs $8. Ryan decides to take his sister to the game as a birthday present. He gives her 1/3 of the money he brought to buy two bleacher tickets and two hot dogs of equal cost. Later, Ryan decides to buy 2 bags of popcorn, which costs $6 total. If Ryan has $34 left. What was the price of one hot dog?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
m = amount of money Ryan brought
m/3 = one third of that amount
If Ryan gives 1/3 of his money to his sister, then he has 2/3 of it left.
m - (m/3) = 1m - (1/3)m = (1-1/3)m = (2/3)m
Note how the fractions 1/3 and 2/3 add to 1.
We subtract off $6 to represent buying the popcorn
(2/3)m - 6
That expression is the amount of money Ryan has left after buying everything mentioned earlier (tickets, hotdogs, popcorn).
We're told he has $34 left, so,
(2/3)m - 6 = 34
(2/3)m = 34+6
(2/3)m = 40
2m = 3*40
2m = 120
m = 120/2
m = 60
Ryan brought $60 with him initially
1/3 of this is 60/3 = 20 dollars
$16 of which goes to the bleacher tickets (since 2*8 = 16).
That leaves 20-16 = 4 dollars left over for the two hotdogs.
Therefore, each hotdog costs 4/2 = 2 dollars.
Answer: 2 dollars
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