Suppose you bought supplies for a party. three rolls of streamers and fifteen party hats cost $30. later, you bought two rolls of streamers and four party hats for $11. write and solve a system of equations to determine the cost of streamers and party hats, find their costs.

The cost of 1 part hat is $ 1.5 and cost of 1 roll of streamer is $ 2.5

Solution:

Let "c" be the cost of each rolls of streamer

Let "p" be the cost of each party hats

Three rolls of streamers and fifteen party hats cost $30

Therefore, we frame a equation as:

Three rolls of streamers x cost of each streamer + fifteen party hats x cost of each party hats = 30

3c + 15p = 30 -------- eqn 1

Later, you bought two rolls of streamers and four party hats for $11

Thus we frame a equation as:

2c + 4p = 11 ------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

6c + 30p = 60 ------ eqn 3

Multiply eqn 2 by 3

6c + 12p = 33 -------- eqn 4

Subtract eqn 4 from eqn 3

6c + 30p = 60

6c + 12p = 33

( - ) --------------

18p = 27

p = 1.5

Substitute p = 1.5 in eqn 2

2c + 4(1.5) = 11

2c + 6 = 11

2c = 5

c = 2.5

Thus cost of 1 part hat is $ 1.5 and cost of 1 roll of streamer is $ 2.5

answer: it is a.,b.,d.

step-by-step explanation: