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erica [24]
3 years ago
10

Students in band are selling oranges and grapefruit to earn money for a trip. Mrs.Whitten purchased three boxes of oranges and t

wo boxes of grapefruit from a student for a total of $22.50. Mr. Rutig purchased one bag of oranges and four boxes of grapefruit, spending a total of $28.50. How much is one box of oranges?
Mathematics
1 answer:
Hitman42 [59]3 years ago
6 0

Answer:

The cost of one box of oranges = $3.3

Step-by-step explanation:

Let x be cost of one box of oranges and y be the cost of one box of grapefruit.

We have been given that Mrs. Whitten purchased 3 boxes of oranges and 2 boxes of grapefruit from a student for a total of $22.50. We can represent this information as:

3x+2y=22.50...(1)  

Mr. Rutig purchased 1 box of oranges and four boxes of grapefruit, spending a total of $28.50. We can represent this information as:

x+4y=28.50...(2)

We will solve our system of linear equations using substitution method.

From equation (1) we will get,

y=\frac{22.50-3x}{2}

Substituting y's value in equation (2) we will get,

x+4*(\frac{22.50-3x}{2})=28.50

x+2*(22.50-3x)=28.50

Upon distributing 2 we will get,

x+45-6x=28.50

x-6x=28.50-45

-5x=-16.5

x=\frac{-16.5}{-5}

x=3.3

Therefore, the cost of one box of oranges is $3.3.

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