Question

student:
applications of percents
lesson 4 student activity sheet
page 3 of 3

1. reinforce you mix 13 1/2 cups of sugar water and 1 1/2 cups of lemon juice. which of the three recipes have you made?
2. reinforce you have 50 cups of mild lemonade. about how many cups of lemon juice do you need to add to make the lemonade super sour?
3. reinforce you want to make mild lemonade but have only 1 cup of lemon juice. what is the greatest amount of mild lemonade you can make?

Explanation:

Problem 8:

Step 1: Find total per recipe

First, find the total cups per recipe by adding sugar water and lemon juice.
Sugar water: $13\frac{1}{2}=\frac{27}{2}$, Lemon juice: $1\frac{1}{2}=\frac{3}{2}$.
Total per recipe: $\frac{27}{2}+\frac{3}{2}=\frac{30}{2}=15$ cups.

Step 2: Multiply by 3 recipes

To find total for 3 recipes, multiply per recipe total by 3.
Total = $15\times3 = 45$ cups.

Answer:

45 cups

Problem 9:

(Assuming the ratio from Problem 8: lemon juice is $1\frac{1}{2}$ cups for some total, but since 50 cups of mild lemonade, we find the ratio of lemon juice to total per recipe first. From Problem 8, total per recipe is 15 cups, lemon juice is $1\frac{1}{2}=\frac{3}{2}$ cups. So ratio of lemon juice to mild lemonade is $\frac{3/2}{15}=\frac{3}{2}\times\frac{1}{15}=\frac{1}{10}$. Now, for 50 cups of mild lemonade, lemon juice needed: $50\times\frac{1}{10}=5$ cups? Wait, maybe the problem is "how much lemon juice to add to make super sour" – but maybe the original ratio is lemon juice : mild lemonade. Wait, maybe the mild lemonade has a certain lemon juice ratio. Wait, maybe the problem is: you have 50 cups of mild lemonade (which has, say, the ratio from Problem 8: lemon juice is $1\frac{1}{2}$ cups for 15 cups of mild lemonade? Wait, no, Problem 8: sugar water $13\frac{1}{2}$ + lemon juice $1\frac{1}{2}$ = 15 cups total (mild lemonade). So lemon juice is $1\frac{1}{2}$ cups in 15 cups of mild lemonade. So ratio of lemon juice to mild lemonade is $\frac{1.5}{15}=0.1$ (10%). So to make super sour, maybe we need to find how much lemon juice to add to 50 cups of mild lemonade. Wait, the problem says "you have 50 cups of mild lemonade. About how many cups of lemon juice do you need to add to make the lemonade super sour?" Maybe the super sour ratio is higher, but maybe the problem is missing info? Wait, maybe it's a typo, or maybe using the ratio from Problem 8. Wait, maybe the original mild lemonade has lemon juice as $1\frac{1}{2}$ cups for 15 cups (from Problem 8: total 15 cups, lemon juice $1\frac{1}{2}$). So 50 cups of mild lemonade: how much lemon juice is already there? Let's calculate:
Lemon juice in 15 cups mild: $1\frac{1}{2}$ cups. So per cup mild lemonade, lemon juice is $\frac{1.5}{15}=0.1$ cups. So in 50 cups, lemon juice already there: $50\times0.1 = 5$ cups. But to make super sour, maybe we need to add more? Wait, the problem is unclear, but maybe the intended question is: if the recipe for mild is 15 cups (13.5 sugar water + 1.5 lemon juice), and we have 50 cups of mild, how much lemon juice to add to make it super sour (maybe double the lemon juice ratio? Or maybe the problem is "how much lemon juice is in 50 cups of mild lemonade" using the ratio from Problem 8. Let's assume that:

Step 1: Find ratio of lemon juice to mild lemonade

From Problem 8: total mild lemonade per recipe = 15 cups, lemon juice = $1\frac{1}{2}$ cups.
Ratio = $\frac{1\frac{1}{2}}{15}=\frac{3/2}{15}=\frac{1}{10}$.

Step 2: Calculate lemon juice in 50 cups

Lemon juice needed (or present) in 50 cups: $50\times\frac{1}{10}=5$ cups.