3. tans spends $\frac{2}{5}$ of her earnings on a phone game. she spends half of her remaining money on music. if her favorite artist’s new album costs $10, how much money did tans have at first?

4. mr. vance gets money for his birthday. he spends $\frac{2}{7}$ of the money on new shoes. he gives the remaining money to 3 different charities. he gives the same amount to each charity.

a. what fraction of his money does mr. vance give to each charity?

b. if mr. vance gives $40 to each charity, how much money did he get for his birthday?

5. leo uses three bags of flour to make cookies. the amount of flour in each bag is the following:
- $\frac{3}{4}$ cups of flour
- $1\frac{1}{2}$ cups of flour
- $1\frac{3}{4}$ cups of flour
each batch of cookies needs $1\frac{1}{4}$ cups of flour. how many batches of cookies can leo make?

6. tyler has a pitcher of $1\frac{3}{4}$ liters of lemonade. tyler pours an equal amount of lemonade into 3 cups. afterward, there is $\frac{1}{2}$ liter of lemonade remaining in the pitcher. how many liters of lemonade are in each cup?

Question

3. tans spends $\frac{2}{5}$ of her earnings on a phone game. she spends half of her remaining money on music. if her favorite artist’s new album costs $10, how much money did tans have at first?

4. mr. vance gets money for his birthday. he spends $\frac{2}{7}$ of the money on new shoes. he gives the remaining money to 3 different charities. he gives the same amount to each charity.

a. what fraction of his money does mr. vance give to each charity?

b. if mr. vance gives $40 to each charity, how much money did he get for his birthday?

5. leo uses three bags of flour to make cookies. the amount of flour in each bag is the following:
- $\frac{3}{4}$ cups of flour
- $1\frac{1}{2}$ cups of flour
- $1\frac{3}{4}$ cups of flour
each batch of cookies needs $1\frac{1}{4}$ cups of flour. how many batches of cookies can leo make?

6. tyler has a pitcher of $1\frac{3}{4}$ liters of lemonade. tyler pours an equal amount of lemonade into 3 cups. afterward, there is $\frac{1}{2}$ liter of lemonade remaining in the pitcher. how many liters of lemonade are in each cup?

Accepted Answer

### Problem 3 (Assuming the first problem about Tans spending money)
# Explanation:
## Step 1: Find remaining money after spending on game
Let total money be $ x $. She spends $ \frac{2}{5}x $ on a game. Remaining money is $ x-\frac{2}{5}x=\frac{3}{5}x $.
## Step 2: Find money spent on clothes (half of remaining)
She spends half of remaining on clothes, so that's $ \frac{1}{2}\times\frac{3}{5}x = \frac{3}{10}x $.
## Step 3: Given she spends $15 on clothes, find total money
If $ \frac{3}{10}x = 15 $, then $ x=15\div\frac{3}{10}=15\times\frac{10}{3}=50 $.
## Step 4: Find money left (total - game - clothes)
Money on game: $ \frac{2}{5}\times50 = 20 $. Money on clothes: 15. Money left: $ 50 - 20 - 15 = 15 $.
# Answer:
The money left is $15.

### Problem 4a (Mr. Perez's money distribution)
# Explanation:
## Step 1: Total fraction spent on shoes and charity
He spends $ \frac{2}{7} $ on shoes and then distributes remaining $ 1 - \frac{2}{7}=\frac{5}{7} $ to 3 charities equally.
## Step 2: Find fraction per charity
Fraction per charity: $ \frac{5}{7}\div3=\frac{5}{7}\times\frac{1}{3}=\frac{5}{21} $.
# Answer:
The fraction is $ \frac{5}{21} $.

### Problem 4b (Mr. Perez's total money)
# Explanation:
## Step 1: Let total money be $ x $
Fraction per charity is $ \frac{5}{21}x $, and it's given as $40. So $ \frac{5}{21}x = 40 $.
## Step 2: Solve for $ x $
$ x = 40\div\frac{5}{21}=40\times\frac{21}{5}=168 $.
# Answer:
He got $168 for his birthday.

### Problem 5 (Leo's flour for cookies)
# Explanation:
## Step 1: Find total flour Leo has
First bag: $ \frac{4}{5} $ cups, second: $ 1\frac{1}{2}=\frac{3}{2} $ cups, third: $ 1\frac{3}{4}=\frac{7}{4} $ cups. Total flour: $ \frac{4}{5}+\frac{3}{2}+\frac{7}{4} $. Find common denominator (20): $ \frac{16}{20}+\frac{30}{20}+\frac{35}{20}=\frac{81}{20} $ cups.
## Step 2: Find number of batches (each batch needs $ 1\frac{3}{4}=\frac{7}{4} $ cups)
Number of batches: $ \frac{81}{20}\div\frac{7}{4}=\frac{81}{20}\times\frac{4}{7}=\frac{81}{35}\approx2.31 $, but since we need whole batches, it's 2 (or if we consider exact fraction, $ \frac{81}{35} $ or $ 2\frac{11}{35} $).
# Answer:
Leo can make $ 2\frac{11}{35} $ batches (or 2 whole batches).

### Problem 6 (Tyler's lemonade in cups)
# Explanation:
## Step 1: Find lemonade poured into cups
Total lemonade: $ 1\frac{3}{4}=\frac{7}{4} $ liters. Remaining: $ \frac{1}{2} $ liters. Poured into cups: $ \frac{7}{4}-\frac{1}{2}=\frac{7}{4}-\frac{2}{4}=\frac{5}{4} $ liters.
## Step 2: Divide by number of cups (3) to find per cup
Per cup: $ \frac{5}{4}\div3=\frac{5}{4}\times\frac{1}{3}=\frac{5}{12} $ liters.
# Answer:
Each cup has $ \frac{5}{12} $ liters of lemonade.

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QUESTION IMAGE

Question

Explanation:

Problem 3 (Assuming the first problem about Tans spending money)

Step 1: Find remaining money after spending on game

Step 2: Find money spent on clothes (half of remaining)

Step 3: Given she spends $15 on clothes, find total money

Step 4: Find money left (total - game - clothes)

Step 1: Total fraction spent on shoes and charity

Step 2: Find fraction per charity

Step 1: Let total money be \( x \)

Step 2: Solve for \( x \)

Answer:

Problem 4a (Mr. Perez's money distribution)