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?

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

Step-by-step 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

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:

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

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.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: