Question

Best Company sells personalized mugs for $18 each plus a fixed fee of $26 for shipping and handling for the entire order. The Cup Expert Company sells personalized mugs for $22 each plus a fixed fee for $14 for shipping and handling for the entire order. How many personalized mugs would a customer have to purchase for the total cost of each company to be the same?

mugs

Answer 1

To find out how many personalized mugs a customer would have to purchase for the total cost from both companies to be the same, we can set up equations for the total cost from each company.

Let \( x \) be the number of mugs purchased.

**For Best Company:**
- Each mug costs $18.
- There is a fixed shipping and handling fee of $26.
- Total cost from Best Company is:
\[
\text{Total cost} = 18x + 26
\]

**For Cup Expert Company:**
- Each mug costs $22.
- There is a fixed shipping and handling fee of $14.
- Total cost from Cup Expert Company is:
\[
\text{Total cost} = 22x + 14
\]

To find the number of mugs \( x \) where the total costs are equal, set the two equations equal to each other:
\[
18x + 26 = 22x + 14
\]

Now, we can solve for \( x \):

1. Subtract \( 18x \) from both sides:
\[
26 = 22x - 18x + 14
\]
\[
26 = 4x + 14
\]

2. Subtract 14 from both sides:
\[
26 - 14 = 4x
\]
\[
12 = 4x
\]

3. Divide both sides by 4:
\[
x = \frac{12}{4} = 3
\]

Thus, a customer would have to purchase **3 mugs** for the total cost from each company to be the same.

Let's verify:
- Total cost from Best Company for 3 mugs:
\[
18(3) + 26 = 54 + 26 = 80
\]

- Total cost from Cup Expert Company for 3 mugs:
\[
22(3) + 14 = 66 + 14 = 80
\]

Both total costs are equal to $80 when purchasing 3 mugs, confirming our solution is correct.