Questions: Elise and her younger brother, Reid, take turns loading the dishwasher after dinner. Because she is older, Elise loads the dishwasher 4 times for every 3 times Reid loads it. If Elise and Reid have loaded the dishwasher 84 times in all this year, how many times has Elise loaded the dishwasher?

Elise and her younger brother, Reid, take turns loading the dishwasher after dinner. Because she is older, Elise loads the dishwasher 4 times for every 3 times Reid loads it.
If Elise and Reid have loaded the dishwasher 84 times in all this year, how many times has Elise loaded the dishwasher?

Transcript text: Elise and her younger brother, Reid, take turns loading the dishwasher after dinner. Because she is older, Elise loads the dishwasher 4 times for every 3 times Reid loads it. If Elise and Reid have loaded the dishwasher 84 times in all this year, how many times has Elise loaded the dishwasher?

Solution

Solution Steps

Step 1: Understand the Problem

Elise and her younger brother, Reid, take turns loading the dishwasher. Elise loads the dishwasher 4 times for every 3 times Reid loads it.

Step 2: Identify the Correct Diagram

The correct diagram should show the ratio of Elise's loads to Reid's loads as 4:3. The first diagram shows Elise loading 4 times and Reid loading 3 times, which matches the given ratio.

Step 3: Calculate the Number of Times Elise Loaded the Dishwasher

Given that Elise and Reid together have loaded the dishwasher 84 times in total, we need to find out how many times Elise has loaded it.

The ratio of Elise's loads to Reid's loads is 4:3. This means for every 7 loads (4+3), Elise loads 4 times and Reid loads 3 times.

To find out how many sets of 7 loads fit into 84: \[ \frac{84}{7} = 12 \]

Each set of 7 loads includes 4 loads by Elise: \[ 12 \times 4 = 48 \]