Questions: Each marble bag sold by Salma's Marble Company contains 4 blue marbles for every 3 purple marbles. If a bag has 24 purple marbles, how many blue marbles does it contain? blue marbles

Each marble bag sold by Salma's Marble Company contains 4 blue marbles for every 3 purple marbles. If a bag has 24 purple marbles, how many blue marbles does it contain?
blue marbles

Transcript text: Each marble bag sold by Salma's Marble Company contains 4 blue marbles for every 3 purple marbles. If a bag has 24 purple marbles, how many blue marbles does it contain? $\square$ blue marbles Check Save For Later Submit Assignm

Solution

Solution Steps

To determine the number of blue marbles in a bag that contains 24 purple marbles, we can use the given ratio of blue to purple marbles (4:3). We can set up a proportion to find the number of blue marbles.

Solution Approach

Identify the ratio of blue to purple marbles, which is 4:3.
Set up a proportion where 4/3 = x/24, where x is the number of blue marbles.
Solve for x by cross-multiplying and dividing.

Step 1: Identify the Ratio

The problem states that each marble bag contains 4 blue marbles for every 3 purple marbles. This gives us the ratio: \[ \frac{\text{blue marbles}}{\text{purple marbles}} = \frac{4}{3} \]

Step 2: Set Up the Proportion

We are given that the bag contains 24 purple marbles. Let $ x $ be the number of blue marbles. We can set up the proportion: \[ \frac{4}{3} = \frac{x}{24} \]

Step 3: Solve for $ x $

To find $ x $, we cross-multiply and solve for $ x $: \[ 4 \times 24 = 3 \times x \] \[ 96 = 3x \] \[ x = \frac{96}{3} \] \[ x = 32 \]