Question

Alana is having a party. She bought 3 rolls of streamers and 2 packages of balloons for $10.00. She realized she needed more supplies and went back to the store and bought 2 more rolls of streamers and 1 more package of balloons for $6.25. How much did each roll of streamers and each package of balloons cost?

Answer 1

Each roll of streamers is $2.50 and each package of balloons is $1.25.

Explanation:

Let x represent the number of rolls of streamers and y represent the number of packages of balloons.

3 rolls of streamers, 3x, and 2 packages of balloons, 2y, cost 10.00; this gives us

3x + 2y = 10

2 rolls of streamers, 2x, and 1 package of balloons, 1y, cost 6.25; this gives us

2x + 1y = 6.25

This gives us the system of equations

`\left \{ {{3x+2y=10} \atop {2x+1y=6.25}} \right.`

To solve this, we will use elimination. First we will make the coefficient of y the same. We will do this by multiplying the bottom equation by 2:

`\left \{ {{3x+2y=10} \atop {2(2x+1y=6.25)}} \right. \\\\\left \{ {{3x+2y=10} \atop {4x+2y=12.50}} \right.`

We will eliminate y by subtracting the bottom equation from the top:

`\left \{ {{3x+2y=10} \atop {-(4x+2y=12.5)}} \right. \\\\-1x=-2.5`

Divide both sides by -1:

-1x/-1 = -2.5/-1

x = 2.5

Each roll of streamers costs $2.50.

Substituting this back into the second equation, we have

2(2.5) + y = 6.25

5 + y = 6.25

Subtract 5 from each side:

5 + y - 5 = 6.25 - 5

y = 1.25

Each package of balloons costs $1.25.