Write a linear system of equations that can be used to solve these problems. Then, solve to get your final answer. I need someone to help me go through this and point me into the correct direction.
5. Matt and Michelle are selling fruit. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large box oranges for a total of $203. Michelle sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost of each small box of oranges and each large box of oranges.
I count 5 posts from you dealing with the same type of problem.
I answered several of those for you, with no response from you.
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To solve this problem, we need to set up a system of linear equations using the given information.
Let's assume the cost of a small box of oranges is 'x' dollars and the cost of a large box of oranges is 'y' dollars.
From the given information, we can derive two equations:
1. The first equation represents the total sales of Matt:
3x + 14y = 203
2. The second equation represents the total sales of Michelle:
11x + 11y = 220
Now, we can solve this system of equations using different methods such as substitution or elimination to find the values of x and y.
Using the substitution method:
We'll solve the second equation for x:
11x = 220 - 11y
x = (220 - 11y) / 11
x = 20 - y
Now, substitute the value of x in the first equation:
3(20 - y) + 14y = 203
60 - 3y + 14y = 203
11y = 203 - 60
11y = 143
y = 143 / 11
y ≈ 13
Substitute this value of y in equation 1:
3x + 14(13) = 203
3x + 182 = 203
3x = 203 - 182
3x = 21
x = 21 / 3
x = 7
So, the cost of each small box of oranges is $7 and the cost of each large box of oranges is $13.
To check the answer, substitute these values of x and y in both equations to ensure they satisfy the given information.
Verification:
For Matt's sales: 3(7) + 14(13) = 21 + 182 = 203
For Michelle's sales: 11(7) + 11(13) = 77 + 143 = 220
Both equations produce the correct total sales, confirming the answer is correct.