At a baseball game, Henry bought five hotdogs and three bags of chips for $14.82. Scott spent a total of $22.89 on seven hotdogs and six bags of chips. Write the system of equations and determine how much each bag of chips cost.
Question
At a baseball game, Henry bought five hotdogs and three bags of chips for 22.89 on seven hotdogs and six bags of chips. Write the system of equations and determine how much each bag of chips cost.
Solution
Let's denote the cost of a hotdog as H and the cost of a bag of chips as C.
From the problem, we can form two equations based on the information given:
- 5H + 3C = 14.82 (This is from Henry's purchase)
- 7H + 6C = 22.89 (This is from Scott's purchase)
This is a system of linear equations. To solve it, we can use either substitution or elimination method. Here, I'll use the elimination method.
First, let's multiply the first equation by 2 and the second equation by 3 to make the coefficients of C the same in both equations:
2*(5H + 3C) = 214.82 3(7H + 6C) = 3*22.89
Which gives us:
10H + 6C = 29.64 21H + 18C = 68.67
Now, subtract the first equation from the second:
(21H + 18C) - (10H + 6C) = 68.67 - 29.64 11H + 12C = 39.03
Simplify this to get:
11H = 39.03 - 12C H = (39.03 - 12C) / 11
Now, substitute H in the first equation (5H + 3C = 14.82):
5((39.03 - 12C) / 11) + 3C = 14.82 (195.15 - 60C) / 11 + 3C = 14.82 17.74 - 5.45C + 3C = 14.82 2.45C = 14.82 - 17.74 2.45C = -2.92 C = -2.92 / 2.45 C = -1.19
The cost of a bag of chips cannot be negative, so there seems to be a mistake in the problem or in the calculations. Please check the numbers in the problem.
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