Solving a word problem using a system of linear equations

Question

A store is having a sale on jelly beans and trail mix. For 2 pds. of jelly beans and 5 pds of trail mix, the total cost is $10. For 8 passengers. of jelly beans and 3pds of trail mix the total cost ic $23. Find the cost for each pd of jelly beans and each pound of trail mix

Answer 1

price of jelly beans = x Use variables to represent the price of the food.

price of trail mix = y

1. 2x + 5y = 10

2. 8x + 3y = 23 I'm assuming it's 8 pounds of jelly beans. There may be a typo error w/ "passengers"

2x = 10 - 5y Set the first equation as x equals to....

x = 5 - 5/2y

Substitute "x = 5 - 5/2y" into the second equation.

8(5 - 5/2y) + 3y = 23

40 - 20y + 3y = 23

40 - 17y = 23

-17y = -17

y = 1

x = 5 - 5/2(1) Plug y =1 into the equation to solve for x.

x = 2.5

Jelly beans are $2.50 a pound and trail mix is $1.00 a pound.