Final Answer:
The cost of a hamburger is $4.00, the cost of an order of fries is $2.00, and the cost of a piece of pie is $1.00.
Step-by-step explanation:
Let H represent the cost of one hamburger, F represent the cost of an order of fries, and P represent the cost of a piece of pie. From the given information, we can form equations based on the cost combinations:
From the equation for the first scenario of one hamburger, 2 orders of fries, and 5 pieces of pie equalling $13.00:
1H + 2F + 5P = $13.00
And from the second scenario of 2 hamburgers and 6 pieces of pie equalling $15.00:
2H + 6P = $15.00
Now, considering the information that the cost of a hamburger is three times the cost of a piece of pie (H = 3P), substitute the value of H into the equations above.
By substitution, we get:
2(3P) + 6P = $15.00
6P + 6P = $15.00
12P = $15.00
P = $1.00
Substitute P = $1.00 back into H = 3P to find the cost of a hamburger:
H = 3 × $1.00 = $3.00
Finally, using the cost of a hamburger, substitute its value into the first equation to find the cost of an order of fries:
1H + 2F + 5P = $13.00
1 × $3.00 + 2F + 5 × $1.00 = $13.00
$3.00 + 2F + $5.00 = $13.00
2F = $13.00 - $8.00
2F = $5.00
F = $2.00
Therefore, the cost of a hamburger is $4.00, the cost of an order of fries is $2.00, and the cost of a piece of pie is $1.00.