| Food | Protein | Cost |
|---|---|---|
| 1 large egg | 6 grams | $0.36 |
| 1 cup of milk | 8 grams | $0.24 |
Based on the table, what is the ratio of the cost per gram of protein in a large egg to the cost per gram of protein in a cup of milk?
For ratio questions involving costs and amounts, first convert each item to a unit rate (cost per 1 unit, such as cost per gram or cost per item). Then, form the ratio in the order the question specifies using those unit rates, and simplify by dividing both parts by the same number. Working in cents instead of dollars (for example, 36 cents and 24 cents) can make mental arithmetic and simplification faster and less error-prone.
Hints
Focus on cost per gram
You are not comparing total costs or total grams directly. First, find the cost per 1 gram of protein for each food.
Compute each unit rate
For each food, divide its cost by its grams of protein. Write two expressions: one for the egg and one for the milk.
Turn unit rates into a ratio
Once you have the cost per gram for each food, place the egg’s cost per gram first and the milk’s cost per gram second to form the ratio, then simplify it.
Desmos Guide
Calculate each cost per gram
In Desmos, type 0.36/6 on one line and 0.24/8 on another. Note the two decimal outputs; these are the egg’s and milk’s costs per gram of protein.
Compare the two unit rates as a ratio
In a new line, enter (0.36/6)/(0.24/8). This gives how many times larger the egg’s cost per gram is than the milk’s. Use this comparison (egg : milk) to choose the matching ratio from the answer choices.
Step-by-step Explanation
Find the egg’s cost per gram of protein
Use the table to write the unit rate (cost per 1 gram of protein) for the egg.
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The egg costs $0.36 and has 6 grams of protein.
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Cost per gram for the egg is
So the egg costs $0.06 per gram of protein.
Find the milk’s cost per gram of protein
Now find the unit rate for the milk.
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The milk costs $0.24 and has 8 grams of protein.
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Cost per gram for the milk is
So the milk costs $0.03 per gram of protein.
Form the ratio egg : milk using the unit rates
The question asks for the ratio of the cost per gram in a large egg to the cost per gram in a cup of milk.
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Egg cost per gram : Milk cost per gram is
To simplify this ratio, divide both parts by :
So the ratio of the cost per gram of protein in a large egg to that in a cup of milk is 2 : 1.