QuestionRosie is making candy bags to give to her friends. The number of lollipops she's including in each bag varies directly with the number of chocolates.
She plans to include 3 lollipops for every 5 chocolates. How many lollipops will she need to buy if she has 75 chocolates? \begin{tabular}{|l|l|} \hline A. 45 & Go to Question \# 6 \\ \hline B. 225 & Go to Question \#8 \\ \hline C. 125 & Go to Question \#1 \\ \hline D. 15 & Go to Question \# 15 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The number of lollipops varies directly with the number of chocolates.
2. Rosie plans to include 3 lollipops for every 5 chocolates.
3. Rosie has 75 chocolates.
4. We need to find out how many lollipops Rosie will need to buy.

STEP 2

1. Understand the direct variation relationship.
2. Set up a proportion based on the given ratio.
3. Solve the proportion to find the number of lollipops.

STEP 3

Understand the direct variation relationship.
The problem states that the number of lollipops varies directly with the number of chocolates. This means that if the number of chocolates increases, the number of lollipops increases in the same ratio.

STEP 4

Set up a proportion based on the given ratio.
Given that Rosie includes 3 lollipops for every 5 chocolates, we can write the proportion as:
$\frac{3 \text{ lollipops}}{5 \text{ chocolates}} = \frac{x \text{ lollipops}}{75 \text{ chocolates}}$
where $x$ is the number of lollipops needed for 75 chocolates.

STEP 5

Solve the proportion to find the number of lollipops.
Cross-multiply to solve for $x$ :
$3 \times 75 = 5 \times x$
$225 = 5x$
Divide both sides by 5 to isolate $x$ :
$x = \frac{225}{5}$
$x = 45$
Rosie will need to buy:
$\boxed{45}$ lollipops.

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