Question

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.

Answer 1

To determine the cost of streamers and party hats, a system of linear equations is created and solved. The streamers cost $2.50 each, and the party hats cost $1.50 each after solving the system by the elimination method.

Step-by-step explanation:

To find the cost of streamers and party hats, we need to set up a system of linear equations based on the information provided. Let's denote the price of one roll of streamers as s and the price of one party hat as h.

From the first purchase:

3s + 15h = $30

From the second purchase:

2s + 4h = $11

Now, we'll solve the system using substitution or elimination method. For simplicity, we'll use the elimination method.

First, let's multiply the second equation by 3.75 to match the number of hats in the first equation:

7.5s + 15h = $41.25

Subtract the first equation from this new equation:

7.5s + 15h - (3s + 15h) = $41.25 - $30

4.5s = $11.25

s = $2.50

With the cost of a streamer found, substitute s = $2.50 into the second original equation:

2($2.50) + 4h = $11

$5 + 4h = $11

4h = $6

h = $1.50

Therefore, the cost of one roll of streamers is $2.50 and the cost of one party hat is $1.50.

Answer 2

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

`3 * c + 15 * p = 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:

`2 * c + 4 * p = 11`

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