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Math

QuestionHow many pitchers of lemonade does Molly need to fill 16 large glasses and 12 small glasses without leftovers?

Studdy Solution

STEP 1

Assumptions1. A pitcher of lemonade can fill exactly6 large glasses or exactly9 small glasses. . Molly wants to serve16 large glasses and12 small glasses.
3. Molly does not want any leftover lemonade.

STEP 2

First, we need to find out how many pitchers are needed to serve the large glasses. We can do this by dividing the total number of large glasses by the number of large glasses that one pitcher can fill.
Pitchers for large glasses=Total large glasses/Large glasses per pitcherPitchers\, for\, large\, glasses = Total\, large\, glasses / Large\, glasses\, per\, pitcher

STEP 3

Now, plug in the given values for the total large glasses and large glasses per pitcher to calculate the number of pitchers needed for the large glasses.
Pitchers for large glasses=16/6Pitchers\, for\, large\, glasses =16 /6

STEP 4

Calculate the number of pitchers needed for the large glasses.
Pitchers for large glasses=16/6=223Pitchers\, for\, large\, glasses =16 /6 =2 \frac{2}{3}

STEP 5

Next, we need to find out how many pitchers are needed to serve the small glasses. We can do this by dividing the total number of small glasses by the number of small glasses that one pitcher can fill.
Pitchers for small glasses=Total small glasses/Small glasses per pitcherPitchers\, for\, small\, glasses = Total\, small\, glasses / Small\, glasses\, per\, pitcher

STEP 6

Now, plug in the given values for the total small glasses and small glasses per pitcher to calculate the number of pitchers needed for the small glasses.
Pitchers for small glasses=12/9Pitchers\, for\, small\, glasses =12 /9

STEP 7

Calculate the number of pitchers needed for the small glasses.
Pitchers for small glasses=12/9=113Pitchers\, for\, small\, glasses =12 /9 =1 \frac{1}{3}

STEP 8

Now that we have the number of pitchers needed for both the large and small glasses, we can add these together to find the total number of pitchers Molly needs to make.
Total pitchers=Pitchers for large glasses+Pitchers for small glassesTotal\, pitchers = Pitchers\, for\, large\, glasses + Pitchers\, for\, small\, glasses

STEP 9

Plug in the values for the pitchers for large glasses and the pitchers for small glasses to calculate the total number of pitchers.
Total pitchers=223+3Total\, pitchers =2 \frac{2}{3} + \frac{}{3}

STEP 10

Calculate the total number of pitchers Molly needs to make.
Total pitchers=223+3=4Total\, pitchers =2 \frac{2}{3} + \frac{}{3} =4Molly needs to make4 pitchers of lemonade.

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