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 18 oz 4 oz
heather 10 oz 3 oz
whose cheesy potatoes have more cheese?
choose one option from each drop - down menu to answer the question.
for every choose oz of potatoes, gary uses choose ounces of cheese than heather. so choose cheesy potatoes have more cheese.
(the drop - down for the first choose has options 15, 10, 20; the other drop - downs have relevant options too)

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	18 oz	4 oz
heather	10 oz	3 oz
whose cheesy potatoes have more cheese?
choose one option from each drop - down menu to answer the question.
for every choose oz of potatoes, gary uses choose ounces of cheese than heather. so choose cheesy potatoes have more cheese.
(the drop - down for the first choose has options 15, 10, 20; the other drop - downs have relevant options too)

Accepted Answer

To solve the problem of determining whose cheesy potatoes have more cheese, we need to calculate the ratio of cheese to potatoes for both Gary and Heather.

### Step 1: Calculate Gary's cheese - to - potato ratio
Gary uses 18 oz of potatoes and 4 oz of cheese. The ratio of cheese to potatoes for Gary is $\frac{4}{18}=\frac{2}{9}\approx0.222$ oz of cheese per oz of potatoes.

### Step 2: Calculate Heather's cheese - to - potato ratio
Heather uses 10 oz of potatoes and 3 oz of cheese. The ratio of cheese to potatoes for Heather is $\frac{3}{10} = 0.3$ oz of cheese per oz of potatoes.

### Step 3: Compare the two ratios
We want to find out for a certain amount of potatoes (let's say we make the amount of potatoes the same for both to compare the cheese) or we can also find out how much cheese each would use for a common amount of potatoes. Let's find out how much cheese Gary would use if he used 10 oz of potatoes (the same as Heather's potato amount).

We know that Gary's ratio is $\frac{4}{18}$ cheese per potato. So for 10 oz of potatoes, Gary would use $10	imes\frac{4}{18}=\frac{40}{18}=\frac{20}{9}\approx2.22$ oz of cheese. Heather uses 3 oz of cheese for 10 oz of potatoes.

Or we can find the amount of potatoes for which the cheese is the same. But another way is to find the unit rate.

Gary's unit rate of cheese per potato: $\frac{4}{18}=\frac{2}{9}\approx0.222$

Heather's unit rate of cheese per potato: $\frac{3}{10} = 0.3$

Since $0.3>0.222$, Heather's cheesy potatoes have more cheese per ounce of potatoes.

But if we want to find for how many ounces of potatoes Gary uses a certain amount compared to Heather:

Let's assume we want to find for $x$ ounces of potatoes, the cheese used by Gary and Heather.

We can also set up a proportion. Let's say we want to find when does Gary's cheese equal Heather's cheese for a given potato amount.

Let $x$ be the amount of potatoes.

Gary's cheese: $y_{G}=\frac{4}{18}x$

Heather's cheese: $y_{H}=\frac{3}{10}x$

We can also find the ratio of the cheese amounts for a common potato amount. Let's take the least common multiple of 18 and 10, which is 90.

For 90 oz of potatoes:

Gary's cheese: $\frac{4}{18}	imes90 = 20$ oz

Heather's cheese: $\frac{3}{10}	imes90=27$ oz

But if we want to find for how many ounces of Heather's potatoes does Gary's cheese compare:

Let's find the amount of potatoes of Heather such that Gary's cheese for that amount of potatoes is compared.

We know that Gary uses 4 oz of cheese for 18 oz of potatoes. Heather uses 3 oz of cheese for 10 oz of potatoes.

Let's find the amount of potatoes of Heather when Gary uses 4 oz of cheese. Wait, maybe the question is about for every how many ounces of potatoes, who has more cheese.

Wait, the drop - down menu has 15, 30, etc. Let's re - examine.

Let's find the ratio of potatoes of Gary to Heather: $\frac{18}{10}=\frac{9}{5}$

Ratio of cheese of Gary to Heather: $\frac{4}{3}$

We want to find for every $x$ ounces of potatoes (Heather's potato amount), how much cheese does Gary use compared to Heather.

Let's set up a proportion. Let's say we want to find $x$ (Heather's potato amount) such that the cheese ratio is compared.

$\frac{4}{18}=\frac{y}{x}$ and $\frac{3}{10}=\frac{y}{x}$? No, better to find the amount of potatoes where we can compare.

Wait, another approach:

We can find the amount of potatoes for which the cheese is the same. Let $4$ (Gary's cheese) be equal to $3	imes k$ (Heather's cheese scaled by $k$) and $18$ (Gary's potatoes) be equal to $10	imes k$ (Heather's potatoes scaled by $k$). But that's not the right way.

Wait, the problem is probably asking: For every [x] ounces of potatoes, Gary uses [y] ounces of cheese, and we need to find x and y to compare.

Wait, let's calculate the ratio of potatoes of Gary to Heather: $\frac{18}{10}=\frac{9}{5}$

Ratio of cheese of Gary to Heather: $\frac{4}{3}$

We can find the least common multiple of 18 and 10, which is 90.

Gary's potatoes: 18, 36, 54, 72, 90

Gary's cheese: 4, 8, 12, 16, 20

Heather's potatoes: 10, 20, 30, 40, 50, 60, 70, 80, 90

Heather's cheese: 3, 6, 9, 12, 15, 18, 21, 24, 27

When Gary uses 90 oz of potatoes, he uses 20 oz of cheese.

When Heather uses 30 oz of potatoes, she uses 9 oz of cheese. Wait, no.

Wait, if we take 30 oz of potatoes:

Gary's cheese for 30 oz of potatoes: $30	imes\frac{4}{18}=\frac{120}{18}=\frac{20}{3}\approx6.67$

Heather's cheese for 30 oz of potatoes: $30	imes\frac{3}{10} = 9$

So Heather uses more cheese.

But if we take 30 oz of potatoes (from the drop - down menu options: 15, 30, 45, etc.):

For 30 oz of potatoes:

Gary's cheese: $\frac{4}{18}	imes30=\frac{120}{18}=\frac{20}{3}\approx6.67$

Heather's cheese: $\frac{3}{10}	imes30 = 9$

Since $9 > 6.67$, Heather's cheesy potatoes have more cheese.

If we consider the drop - down menu with options 15, 30, etc.

For 30 oz of potatoes:

Gary's cheese: $30	imes\frac{4}{18}=\frac{20}{3}\approx6.67$

Heather's cheese: $30	imes\frac{3}{10}=9$

So Heather's cheesy potatoes have more cheese.

So the answer is: For every 30 ounces of potatoes, Gary uses $\frac{20}{3}\approx6.67$ ounces of cheese and Heather uses 9 ounces of cheese. So Heather's cheesy potatoes have more cheese.

If we are to fill the drop - down:

For every 30 ounces of potatoes, Gary uses $\frac{20}{3}\approx6.67$ (but the drop - down has options, maybe we made a mistake. Wait, let's recalculate the ratio of cheese per potato.

Gary: $\frac{4}{18}=\frac{2}{9}\approx0.222$

Heather: $\frac{3}{10} = 0.3$

Let's find how much cheese Gary uses for 15 ounces of potatoes: $15	imes\frac{4}{18}=\frac{60}{18}=\frac{10}{3}\approx3.33$

Heather for 15 ounces of potatoes: $15	imes\frac{3}{10}=4.5$

For 30 ounces of potatoes:

Gary: $30	imes\frac{4}{18}=\frac{120}{18}=\frac{20}{3}\approx6.67$

Heather: $30	imes\frac{3}{10} = 9$

For 45 ounces of potatoes:

Gary: $45	imes\frac{4}{18}=10$

Heather: $45	imes\frac{3}{10}=13.5$

We can see that as the amount of potatoes increases, the difference in cheese between Heather and Gary also increases.

But the problem is asking "Whose cheesy potatoes have more cheese?"

Since $\frac{3}{10}>\frac{2}{9}$ (because $\frac{3}{10}=0.3$ and $\frac{2}{9}\approx0.222$), Heather's cheesy potatoes have more cheese per ounce of potatoes.

If we consider the drop - down menu for "For every [x] ounces of potatoes, Gary uses [y] ounces of cheese" and we want to find x and y to compare:

Let's find the amount of potatoes where we can express the cheese in a simple fraction.

We can find the ratio of potatoes of Gary to Heather: $\frac{18}{10}=\frac{9}{5}$

Ratio of cheese of Gary to Heather: $\frac{4}{3}$

We can cross - multiply: $4	imes10 = 40$ and $3	imes18=54$. Since $40 < 54$, Heather's cheese per potato is more.

So, Heather's cheesy potatoes have more cheese.

If we are to fill the drop - down:

Let's assume we want to find for 30 ounces of potatoes (since 18 and 10 have a least common multiple of 90, but 30 is a multiple of 10 and 18/3 = 6, 10*3 = 30).

For 30 ounces of potatoes:

Gary's cheese: $30	imes\frac{4}{18}=\frac{120}{18}=\frac{20}{3}\approx6.67$

Heather's cheese: $30	imes\frac{3}{10}=9$

Since $9>6.67$, Heather's cheesy potatoes have more cheese.

So the answer is that Heather's cheesy potatoes have more cheese. If we consider the drop - down options, for every 30 ounces of potatoes, Gary uses $\frac{20}{3}\approx6.67$ ounces of cheese and Heather uses 9 ounces of cheese, so Heather's have more.

# Answer:
Heather's cheesy potatoes have more cheese. If we consider the drop - down menu context, for example, for every 30 ounces of potatoes, Gary uses $\frac{20}{3}\approx6.67$ ounces of cheese and Heather uses 3 ounces of cheese per 10 ounces of potatoes (or 9 ounces per 30 ounces of potatoes), so Heather's have more cheese. The final answer is that Heather's cheesy potatoes have more cheese.

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QUESTION IMAGE

Question

Explanation:

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

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

Step 3: Compare the two ratios

Answer: