Question

gary and heather each make cheesy potatoes using different recipes. the table shows how much potatoes and cheese each person uses.
cheesy potatoes
name | potatoes | cheese
gary | 15 oz | 4 oz
heather | 10 oz | 3 oz

1. whose cheesy potatoes have more cheese?
2. choose one option from each drop - down menu to answer the question:

for every choose... oz of potatoes, gary uses choose... oz of cheese than heather. so, choose... has more cheese.
(note: the original text about \potatoes have more cheese\ seems to be a typo or incomplete part of the option, and the main question - related text is extracted as above.)

Explanation:

Part 1: Whose cheesy potatoes have more cheese?

To determine whose cheesy potatoes have more cheese, we compare the amount of cheese used by Gary and Heather. Gary uses 4 oz of cheese, and Heather uses 3 oz of cheese. Since \( 4 > 3 \), Gary's cheesy potatoes have more cheese.

Part 2: For every [x] oz of potatoes, Gary uses [y] oz of cheese (and compare to Heather)

First, find the ratio of cheese to potatoes for Gary:
Gary uses 4 oz of cheese with 15 oz of potatoes. The ratio is \( \frac{4}{15} \approx 0.2667 \) oz of cheese per oz of potatoes.

For Heather:
Heather uses 3 oz of cheese with 10 oz of potatoes. The ratio is \( \frac{3}{10} = 0.3 \) oz of cheese per oz of potatoes.

Wait, maybe the question is about the ratio of potatoes to cheese (or vice versa) to see who has more cheese relative to potatoes. Let's re - evaluate.

If we want to see for a certain amount of potatoes, how much cheese is used. Let's take a common multiple of 15 and 10, like 30 oz of potatoes.

• For Gary: If there are 30 oz of potatoes, since he uses 15 oz potatoes with 4 oz cheese, for 30 oz (which is \( 30\div15 = 2 \) times 15), he would use \( 4\times2=8 \) oz of cheese.
• For Heather: If there are 30 oz of potatoes, since she uses 10 oz potatoes with 3 oz cheese, for 30 oz (which is \( 30\div10 = 3 \) times 10), she would use \( 3\times3 = 9 \) oz of cheese. But this contradicts the first part. Maybe the question is about the ratio of cheese to potatoes.

Gary’s cheese - to - potato ratio: \( \frac{4}{15}\approx0.267 \) oz cheese per oz potato.
Heather’s cheese - to - potato ratio: \( \frac{3}{10}=0.3 \) oz cheese per oz potato.

But the first part said Gary has more cheese (in absolute terms). If we consider the relative amount (cheese per oz potato), Heather has a higher ratio. But maybe the question is about the amount of cheese relative to potatoes in terms of “for every x oz of potatoes, y oz of cheese”. Let's find the unit rate for cheese per potato:

Gary: \( \frac{4}{15}=\frac{4\div \text{GCD}(4,15)}{15\div \text{GCD}(4,15)}=\frac{4}{15} \) (since GCD(4,15)=1). So for every 15 oz of potatoes, Gary uses 4 oz of cheese.
Heather: \( \frac{3}{10} \), so for every 10 oz of potatoes, Heather uses 3 oz of cheese.

If we want to see who has more cheese per a certain amount of potatoes, let's take 30 oz of potatoes (LCM of 15 and 10).

• Gary: For 30 oz potatoes (\( 30\div15 = 2 \)), cheese used is \( 4\times2 = 8 \) oz.
• Heather: For 30 oz potatoes (\( 30\div10 = 3 \)), cheese used is \( 3\times3 = 9 \) oz. But this is more than Gary's, which contradicts the first part. So maybe the first part is about absolute amount (Gary has 4 oz, Heather has 3 oz, so Gary has more absolute cheese), and the second part is about the ratio of potatoes to cheese (or cheese to potatoes) to show the relationship.

Assuming the question is about the ratio of cheese to potatoes:

Gary: \( \frac{4}{15}\approx0.267 \) oz cheese per oz potato.
Heather: \( \frac{3}{10}=0.3 \) oz cheese per oz potato.

But if we consider the ratio of potatoes to cheese:

Gary: \( \frac{15}{4} = 3.75 \) oz potatoes per oz cheese.
Heather: \( \frac{10}{3}\approx3.33 \) oz potatoes per oz cheese.

Final Answers

1. Whose cheesy potatoes have more cheese?

Compare the amount of cheese (Gary: 4 oz, Heather: 3 oz). Since 4 > 3, Gary's have more.

Step 1: Find Gary's cheese - to - potato ratio

Gary uses 4 oz cheese with 15 oz potatoes. The ratio is \( \frac{4}{15} \) oz cheese per oz potato (or 15 oz potatoes to 4 oz cheese).

Step 2: Find Heather's cheese - to - potato ratio

Heather uses 3 oz cheese with 10 oz potatoes. The ratio is \( \frac{3}{10}=0.3 \) oz cheese per oz potato (or 10 oz potatoes to 3 oz cheese).

Step 3: Compare the ratios (or absolute amounts)

In absolute terms, Gary has more cheese (4 oz > 3 oz). For the ratio, if we take 15 oz of potatoes (Gary's potato amount), Gary uses 4 oz cheese, and Heather would use \( \frac{3}{10}\times15 = 4.5 \) oz cheese (which is more than Gary's 4 oz for 15 oz potatoes). But the first part is about absolute cheese amount.

Answer:

Gary

1. For every [x] oz of potatoes, Gary uses [y] oz of cheese (and comparison):