Question

Roger and Trevor went shopping for produce on the same day. They each bought some apples and some potatoes. The amount they bought and the total price they paid listed in the table below Roger, apple(Ib) 8, potatoes(Ib) 7, total cost ($) 18.85 Trevor, apples(Ib) 2, potatoes(Ib) 10, total cost($) 12.88 What was the price of apples and potatoes per pound?

Answer 1

Let x be price of apples per pound and y be price of potatoes per pound.

We can set a system of equations by our given information as:

$8x+7y=18.85...(1)$

$2x+10y=12.88...(2)$

Now we will use substitution method to solve our system of equations.

From equation 2 we will get,

$x=\frac{12.88-10y}{2}$

Upon substituting value of x in equation 1 we will get,

$8\cdot(\frac{12.88-10y}{2} )+7y=18.85$

$4\cdot(12.88-10y)+7y=18.85$  

$51.52-40y+7y=18.85$

$-33y=18.85-51.52$

$-33y=-32.76$

$33y=32.76$

$y=\frac{32.76}{33} =0.99$

Therefore, price of potatoes will be $0.99 per pound.

Now let us find price of apples by substituting y=0.99 in equation 2.

$2x+10\cdot0.99=12.88$

$2x+9.9=12.88$

$2x=12.88-9.9$

$2x=2.98$

$x=\frac{2.98}{2} =1.49$

Therefore, price of apples will be $1.49 per pound.