Question
Shirts-2-Go sells t-shirts for a base price of $12 per shirt plus a fixed fee of $3 shipping and handling for the whole order. Shirts PLUS sells t-shirts for a base price of $8 per shirt plus a fixed fee of $23 shipping and handling for the whole order. Let x represent the number of shirts ordered and let y represent the total cost of the order.
y = 12x + 3
y = 8x + 23
How many shirts would you have to purchase for the total cost to be the same at both companies?
shirts
y = 12x + 3
y = 8x + 23
How many shirts would you have to purchase for the total cost to be the same at both companies?
shirts
Answers
GPT-4o mini
To find the number of shirts where the total costs from both companies are the same, we need to set the two equations equal to each other:
\[
12x + 3 = 8x + 23
\]
Now, let's solve for \(x\):
1. Subtract \(8x\) from both sides:
\[
12x - 8x + 3 = 23
\]
This simplifies to:
\[
4x + 3 = 23
\]
2. Now, subtract 3 from both sides:
\[
4x = 20
\]
3. Finally, divide by 4:
\[
x = 5
\]
Thus, you would have to purchase **5 shirts** for the total cost to be the same at both companies.
\[
12x + 3 = 8x + 23
\]
Now, let's solve for \(x\):
1. Subtract \(8x\) from both sides:
\[
12x - 8x + 3 = 23
\]
This simplifies to:
\[
4x + 3 = 23
\]
2. Now, subtract 3 from both sides:
\[
4x = 20
\]
3. Finally, divide by 4:
\[
x = 5
\]
Thus, you would have to purchase **5 shirts** for the total cost to be the same at both companies.