Question
Brittany is comparing the cost of buying coffee VS buying a fancy coffee Maker.She usually spends 650 per cup at Starbucks.And it has a $50 gift card.She is considering buying a coffee Maker.That is $200, so she can easily make coffee from home.Then the coffee would be cost 55 cents per cup.How many coffees would she have to buy for both options to be the same cost and why
Answers
GPT-4o mini
To determine how many cups of coffee Brittany would need to buy from Starbucks for the cost of buying coffee to equal the cost of buying a coffee maker, we need to set up an equation for both options.
1. **Cost of buying from Starbucks:**
- Cost per cup = $6.50
- She has a $50 gift card, which will reduce her total spending.
- Let \( x \) be the number of cups she buys.
- Total cost for \( x \) cups before using the gift card = \( 6.50x \)
- After using the gift card, her total cost will be:
\[
\text{Cost from Starbucks} = 6.50x - 50
\]
2. **Cost of buying a coffee maker:**
- Cost of the coffee maker = $200
- Cost per cup (once she has the coffee maker) = $0.55
- Total cost for \( x \) cups after buying the coffee maker:
\[
\text{Cost from coffee maker} = 200 + 0.55x
\]
3. **Set the costs equal to find \( x \):**
\[
6.50x - 50 = 200 + 0.55x
\]
4. **Solve the equation:**
- First, rearranging gives:
\[
6.50x - 0.55x = 200 + 50
\]
\[
5.95x = 250
\]
- Now, divide both sides by 5.95 to solve for \( x \):
\[
x = \frac{250}{5.95} \approx 42.02
\]
Since \( x \) must be a whole number (you can't buy a fraction of a cup of coffee), Brittany would need to buy **at least 43 cups of coffee from Starbucks** for the costs of both options to be the same.
**Summary:**
Brittany would have to buy approximately **43 cups** from Starbucks for the total costs of buying coffee and using the coffee maker to be equal, considering the gift card and the cost per cup.
1. **Cost of buying from Starbucks:**
- Cost per cup = $6.50
- She has a $50 gift card, which will reduce her total spending.
- Let \( x \) be the number of cups she buys.
- Total cost for \( x \) cups before using the gift card = \( 6.50x \)
- After using the gift card, her total cost will be:
\[
\text{Cost from Starbucks} = 6.50x - 50
\]
2. **Cost of buying a coffee maker:**
- Cost of the coffee maker = $200
- Cost per cup (once she has the coffee maker) = $0.55
- Total cost for \( x \) cups after buying the coffee maker:
\[
\text{Cost from coffee maker} = 200 + 0.55x
\]
3. **Set the costs equal to find \( x \):**
\[
6.50x - 50 = 200 + 0.55x
\]
4. **Solve the equation:**
- First, rearranging gives:
\[
6.50x - 0.55x = 200 + 50
\]
\[
5.95x = 250
\]
- Now, divide both sides by 5.95 to solve for \( x \):
\[
x = \frac{250}{5.95} \approx 42.02
\]
Since \( x \) must be a whole number (you can't buy a fraction of a cup of coffee), Brittany would need to buy **at least 43 cups of coffee from Starbucks** for the costs of both options to be the same.
**Summary:**
Brittany would have to buy approximately **43 cups** from Starbucks for the total costs of buying coffee and using the coffee maker to be equal, considering the gift card and the cost per cup.