Question

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

Answer 1

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=(22.50-3x)/(2)`

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

`x+4*((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=(-16.5)/(-5)`

`x=3.3`

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