Question
The Raging Tigers are considering using one of two companies to print their team shirts for an upcoming tournament. Their first option is to pay CiTee's a fee of $50 for the logo design and $5 per shirt for printing.
y = 5x + 50
Their second option is to pay a fee of $30 to PrintWithUs for the logo design and $10 per shirt for printing.
y = 10x + 30
The costs of the two printing companies are shown in the graph.
How many shirts must be printed for the costs of the two printing companies to be the same?
y = 5x + 50
Their second option is to pay a fee of $30 to PrintWithUs for the logo design and $10 per shirt for printing.
y = 10x + 30
The costs of the two printing companies are shown in the graph.
How many shirts must be printed for the costs of the two printing companies to be the same?
Answers
GPT-4o mini
To find the number of shirts where the costs of the two printing companies are the same, we need to set the equations for the costs equal to each other and solve for \( x \), where \( x \) is the number of shirts printed.
The cost equations are:
1. For CiTee's:
\[ y = 5x + 50 \]
2. For PrintWithUs:
\[ y = 10x + 30 \]
Set the two equations equal to each other:
\[
5x + 50 = 10x + 30
\]
Now, solve for \( x \):
1. Subtract \( 5x \) from both sides:
\[ 50 = 5x + 30 \]
2. Next, subtract 30 from both sides:
\[ 20 = 5x \]
3. Finally, divide both sides by 5:
\[ x = 4 \]
So, the costs of the two printing companies will be the same when 4 shirts are printed.
The cost equations are:
1. For CiTee's:
\[ y = 5x + 50 \]
2. For PrintWithUs:
\[ y = 10x + 30 \]
Set the two equations equal to each other:
\[
5x + 50 = 10x + 30
\]
Now, solve for \( x \):
1. Subtract \( 5x \) from both sides:
\[ 50 = 5x + 30 \]
2. Next, subtract 30 from both sides:
\[ 20 = 5x \]
3. Finally, divide both sides by 5:
\[ x = 4 \]
So, the costs of the two printing companies will be the same when 4 shirts are printed.