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

Hello!

You can make two expressions based on what you know

let x represent the cost of balloons
let y represent the cost of streamers

2x + 3y = 10
x + 2y = 6.25

you can multiply the second equation by 2

2x + 4y = 12.50

You can subtract the two equations from each other to get y

-y = -2.50

Since y is negative we can multiply both sides by -1 to make y positive

y = 2.50

streamers cost 2.50 each

Now we plug this into one of the original equations to get the cost of balloons

x + 2(2.50) = 6.25

Multiply

x + 5 = 6.25

Subtract 5 from both sides

x = 1.25

The answers are
1 package of balloons cost $1.25
1 roll of streamers cost $2.50

Hope this helps!

Answer 2

3 rolls of steamer + 2 packages of balloons = $10 -------------- (1)
2 rolls of steamer + 1 package of balloons = $6.25 --------- (2)

(2) x 2:
4 rolls of steamer + 2 package of balloons = $12.50 --------- (2a)

(2a) - (1):
1 roll of steamer = $2.50 ----------- Sub into (1)
3 ($2.50) + 2 packages of balloons = $10
$7.50 + 2 packages of balloons = $10
2 packages of balloons = $10 - $7.50
2 packages of balloons = $2.50
1 packages of balloons = $1.25

1 packages of balloons = $1.25
1 roll of steamer = $2.50

1 packages of balloons + 1 roll of steamer = $1.25 + $2.50 = $3.75