Respuesta :
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:
[tex]3x+2y=22.50...(1)[/tex]
Mr. Rutig purchased 1 box of oranges and four boxes of grapefruit, spending a total of $28.50. We can represent this information as:
[tex]x+4y=28.50...(2)[/tex]
We will solve our system of linear equations using substitution method.
From equation (1) we will get,
[tex]y=\frac{22.50-3x}{2}[/tex]
Substituting y's value in equation (2) we will get,
[tex]x+4*(\frac{22.50-3x}{2})=28.50[/tex]
[tex]x+2*(22.50-3x)=28.50[/tex]
Upon distributing 2 we will get,
[tex]x+45-6x=28.50[/tex]
[tex]x-6x=28.50-45[/tex]
[tex]-5x=-16.5[/tex]
[tex]x=\frac{-16.5}{-5}[/tex]
[tex]x=3.3[/tex]
Therefore, the cost of one box of oranges is $3.3.
