Ahmed and Christy are selling boxes of fruit for a Habitat for Humanity fundraiser. Customers can buy small boxes of fruit and large boxes of fruit. Ahmed sold 24 small boxes of fruit and 14 large boxes of fruit for a total of $337.00. Christy sold 21 small boxes of fruit and 16 large boxes of fruit for a total of $353.00. Find the cost of one small box of fruit and the cost of one large box of fruit.

The cost of one small box of fruit is $5.00 and the cost of one large box of fruit is $15.50

Step-by-step explanation:

Let

x ----> the cost of one small box of fruit

y ----> the cost of one large box of fruit

we know that

Ahmed

Ahmed sold 24 small boxes of fruit and 14 large boxes of fruit for a total of $337.00.

so

-----> equation A

Christy

Christy sold 21 small boxes of fruit and 16 large boxes of fruit for a total of $353.00

so

----> equation B

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (5,15.5)

see the attached figure

therefore

The cost of one small box of fruit is $5.00 and the cost of one large box of fruit is $15.50

option a is correct.

only one solution to the system of equations

step-by-step explanation:

if the graph of the equations do not intersects(i.,e if they are parallel) then, there are no solutions that are true for both the equations.

if the graph of the equations intersects, then there is one solution and that is true for both the equations.

since, in the given figure:

the two lines intersect each other

⇒there is only one solution which satisfy both the lines of an equations.

therefore, there is only one solution to the system of equation