Question

A fruit stand has to decide what to charge for their produce. They need \$10$10 for 44 apples and 44 oranges. They also need \$15$15 for 66 apples and 66 oranges. We put this information into a system of linear equations. Can we find a unique price for an apple and an orange?

Answer 1

no;has many solutions

Explanation:

Answer 2

We can't find a unique price for an apple and an orange.

Explanation:

Suppose, the price of an apple is
`x` and the price of an orange is
`y`

They need $10 for 4 apples and 4 oranges. So, the first equation will be.......

`4x+4y=10 ........................................(1)`

They also need $15 for 6 apples and 6 oranges. So, the second equation will be........

`6x+6y= 15 ........................................(2)`

Dividing equation (1) by 2 on both sides :
`2x+2y= 5`

Dividing equation (2) by 3 on both sides :
`2x+2y=5`

So, we can see that both equation (1) and (2) are actually same. That means, we will not get any unique solution for
`x` and
`y` here. Both
`x` and
`y` have "infinitely many solutions".

Thus, we can't find a unique price for an apple and an orange.