Question

A fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges.

They also need $12 for 6 apples and 6 oranges. We put this information into a system of linear equations,

Can we find a unique price for an apple and an orange?

A. Yes; they should charge $1.00 for an apple and $1.50 for an orange

B. Yes; they should charge for $1.00 for an apple and $1.00 for an orange

C. No; the system has many solutions

D. No; the system has no solution

(This is from Khan academy)

Answer 1

Given 4 apples and 4 oranges cost = $10.

6 apples and 6 oranges = $12.

Let us assume cost of each apple = $x.

Cost of each orange = $y.

4 apples and 4 oranges cost can be given by equation:

4x+4y = 10.

Dividing both sides by 4, we get

x+y = 2.50 ---------------equation (1)

6 apples and 6 oranges cost can be given by equation:

6x+6y = 12.

Dividing both sides by 6, we get

x+y =2 ---------------equation (2).

We can see from equation (1) and equation (2), that x+y equals 2 and 2.5.

But that doesn't seem to be true.

So, we could just say that we can't find a unique price for an apple and an orange for the given information.