Erik and Amanda are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Erik sold 25 small boxes of fruit and 14 large boxes of fruit for a total of $402.00. Amanda sold 21 small boxes of fruit and 12 large boxes of fruit for a total of $342.00. Find the cost of one small box of fruit and the cost of one large box of fruit.

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ChiKesselman ChiKesselman · Answer 1 · 2019-10-07T10:29:51+02:00

Answer:

Cost of smaller box is $6.00 and cost of larger box is $18.00

Step-by-step explanation:

We are given the following information in the question:

Let x be the cost of small boxes and y be the cost of larger fruit boxes.

Eric sold 25 small boxes and 14 large boxes for $402.00

This can be written in the form of expression:

[tex]25x + 14 y = 402[/tex]

Amanda sold 21 small boxes and 12 large boxes for $342.00

This can be interpreted with the expression:

[tex]21x + 12y = 342[/tex]

Now, we have two equations in two variables. Thus, solving these equations with the help of substitution method:

[tex]25x + 14(\frac{342 - 21x}{12}) = 402[/tex]

Solving this equation, we have x= 6.

Putting this value of x in any of the equation, we get,

[tex](21)(6) + 12y =342\\y = 18[/tex]

Therefore, cost of smaller box is $6.00 and cost of larger box is $18.00