Application solve

Question

At the amusement park Dustin bought 1 hot dog, 2 popcorns, and 3 sodas. Dustin spent $15.25. Luis spent $14 and bought 2 hot dogs and 3 sodas. Marci got 1 hot dog, 2 popcorns and 1 soda and spent $10.25. How much did each snack cost?

Answer 1

Let's use the variable h to represent the cost of one hot dog, the variable p to represent the cost of one popcorn, and the variable s to represent the cost of one soda.

Now we can write three equations with three unknowns to represent the purchases made:

For Dustin: 1 h + 2 p + 3 s = $15.25

For Luis: 2 h + 3 s = 14

For Marci: 1 h + 2 p + 1 s = 10.25

We can use elimination to solve for s using Dustin's equation and Marci's equations. Multiply Marci's equation by -1:

1 h + 2 p + 3 s = 15.25

-1 h - 2 p - 1 s = -10.25

2 s = 5.00

s = 2.50

Each soda will cost $2.50

Now substitute $2.50 for s in Luis' equation and solve for h (the cost of one hot dog):

2 h + 3 s = 14

2 h + 3 * 2.50 = 14

2 h + 7.50 = 14

2 h + 7.50 - 7.50 = 14 -7.50

2h = 6.50

h = 3.25

Each hot dog will cost $3.25

Then substitute the cost of a hot dog and a soda in Marci's equation and solve for the cost of a popcorn(p):

1 h + 2 p + 1 s = 10.25

1 * 3.25 + 2 p + 1*2.50 = 10.25

2 p + 5.75 = 10.25

2 p + 5.75 - 5.75 = 10.25 - 5.75

2 p = 4.50

p = 2.25

Each popcorn will cost $2.25