A smoothie recipe calls for 1 cup of yogurt, 1 pint of strawberries, and 2 cups of orange juice. If we want to maintain the same ingredient proportions but make a larger batch that uses 3 gallons of orange juice, how many cups of yogurt and pints of strawberries will we need?

To maintain the same ingredient proportions when scaling up the recipe, you need to find the ratio of the original recipe and then apply that ratio to the larger quantity of orange juice.

Original recipe: 1 cup of yogurt

1 pint of strawberries

2 cups of orange juice

Let’s find the ratio of each ingredient to the orange juice:

\$ 3 \times 16 = 48 "cups" \$

Ratio of Yogurt to Orange Juice: 1 cup: 2 cups = \$1/2\$ cups

Strawberries to Orange Juice: 1 pint : 2 cups = \$(1 "pint") /(2 "cups")\$

Now, you want to use 3 gallons of orange juice, and 1 gallon is equivalent to 16 cups. So, 3 gallons is \$3 times 16 = 48 "cups"\$.

Now, apply the ratios to the larger quantity of orange juice:

Yogurt: 1 cup : 2 cups = X cups : 48 cups

Solving for X :\$ 1/2 times 48\$ = 24 cups of yogurt.

Now, apply the ratios to the larger quantity of orange juice:

Strawberries: 1 pint : 2 cups = Y pints : 48 cups

Solving for Y =\$ 1/2 times 48 \$ = 24 pints of strawberries.

So, to make a larger batch using 3 gallons of orange juice, you will need 24 cups of yogurt and 24 pints of strawberries.

Answer

A