To solve this problem, we need to determine the cost of one roll of crepe paper given the information about the two purchases. Let the cost of one roll of crepe paper be $x$ dollars and the cost of one balloon be $y$ dollars.

1. Translate the information into equations:

From the problem:

• In the first purchase, you buy 6 rolls of crepe paper and 20 balloons for $11.90.
  This gives the equation:
  $6x + 20y = 11.90$

• In the second purchase, you buy 2 rolls of crepe paper and 15 balloons for $6.05.
  This gives the equation:
  $2x + 15y = 6.05$

2. Solve the system of equations:

We now have two equations:

1. $6x + 20y = 11.90$
2. $2x + 15y = 6.05$

Step 1: Eliminate $x$ or $y$ using elimination or substitution.

To eliminate $x$, multiply the second equation by 3 so the coefficient of $x$ matches the first equation:

$3(2x + 15y) = 3(6.05)$ $6x + 45y = 18.15$

Now subtract the first equation $6x + 20y = 11.90$ from $6x + 45y = 18.15$:

$(6x + 45y) - (6x + 20y) = 18.15 - 11.90$ $25y = 6.25$

Solve for $y$:

$y = \frac{6.25}{25} = 0.25$

Thus, the cost of one balloon is $y = 0.25$ dollars.

Step 2: Solve for $x$ (cost of one roll of crepe paper):

Substitute $y = 0.25$ into the second equation $2x + 15y = 6.05$:

$2x + 15(0.25) = 6.05$ $2x + 3.75 = 6.05$

Subtract 3.75 from both sides:

$2x = 6.05 - 3.75$ $2x = 2.30$

Solve for $x$:

$x = \frac{2.30}{2} = 1.15$

Thus, the cost of one roll of crepe paper is $1.15.

Final Answer:

The cost of each roll of crepe paper is $1.15.

Do you want me to explain any step further or verify with another method? Let me know!

Related Questions:

1. What is the total cost of 10 rolls of crepe paper and 30 balloons?
2. How much would 8 rolls of crepe paper and 12 balloons cost?
3. What is the cost of 50 balloons alone?
4. If the price of balloons increases by $0.10, how would that affect the total cost of the first purchase?
5. How can you solve this problem using matrices?

Tip: When solving systems of equations, organize your steps clearly to avoid errors!