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

Answer:

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

Step-by-step 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.