Question

Ryan bought 6 apples and 9 peaches for a total of $7.86. Madi bought 4 apples and 5 peaches for $4.82.

Answer 1

Let's call:
a = price of 1 apple
p = price of 1 peach

The total cost is the price of 1 apple times the number of apples plus the price of 1 peach times the number of peaches, therefore the system can be:
$\left \{ {{6a + 9p = 7.86} \atop {4a + 5p = 4.82}} \right.$

Solve for a in the second equation (you can choose to solve for any of the variables in any of the equations, try to understand what is the best):
a = (4.82 - 5p) / 4

Now, substitute in the first equation:
6 · (4.82 - 5p) / 4 + 9p = 7.86
7.23 - (15/2)p + 9p = 7.86
(3/2)p = 0.63
p = 0.42

Now, substitute this value in the formula found for a:
a = (4.82 - 5·0.42) / 4
   = 0.68

Therefore, one apple costs 0.68$ and one peach costs 0.42$.