Question

A fruit stand has to decide what to charge for their produce. They decide to charge \$5.30$5.30 for 11 apple and 11 orange. They also plan to charge \$14$14 for 22 apples and 22 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, we can not find a unique price for an apple and an orange.

Explanation:

Let x be the price of each apple and y be the price of each orange.

We have been given that a fruit stand charge $5.30 for 1 apple and 1 orange. We can represent this information as:

`x+y=5.30...(1)`

We are also told that they plan to charge $14 for 2 apples and 2 oranges. We can represent this information as:

`2x+2y=14...(2)`

Upon dividing equation (2) by 2 we will get,

`x+y=7...(2)`

Upon converting our equations into slope-intercept form we will get,

`y=-x+5.30`

`y=-x+7`

We can see that slope for both lines in -1, but both lines have different y-intercept, so these lines are parallel lines.

Since parallel lines do not intersect, therefore, we can not find a unique price for an apple and an orange.