Question

1. tara spends \\(\frac{2}{3}\\) of her money on a video game. she spends half of her remaining money on lunch. if her lunch costs $10, how much money did tara have at first?
2. mr. perez gets money for his birthday. he spends \\(\frac{1}{3}\\) 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. perez give to each charity?
b. if mr. perez gives $60 to each charity, how much money did he get for his birthday?

Explanation:

Problem 3

Step 1: Find remaining money after video game

Let initial money be \( x \). After spending \( \frac{3}{4}x \) on video game, remaining money is \( x - \frac{3}{4}x=\frac{1}{4}x \).

Step 2: Relate lunch cost to remaining money

She spends half of remaining money on lunch, so lunch cost is \( \frac{1}{2}\times\frac{1}{4}x=\frac{1}{8}x \). Given lunch cost is $10, so \( \frac{1}{8}x = 10 \).

Step 3: Solve for initial money \( x \)

Multiply both sides by 8: \( x = 10\times8 = 80 \).

Step 1: Find remaining money after shoes

Let total money be \( y \). After spending \( \frac{1}{3}y \) on shoes, remaining money is \( y-\frac{1}{3}y=\frac{2}{3}y \).

Step 2: Find fraction per charity

He gives remaining money to 3 charities equally, so per charity fraction is \( \frac{2}{3}y\div3=\frac{2}{3}y\times\frac{1}{3}=\frac{2}{9}y \), so fraction is \( \frac{2}{9} \).

Step 1: Relate charity amount to total money

From 4a, each charity gets \( \frac{2}{9}y \). Given each charity gets $60, so \( \frac{2}{9}y = 60 \).

Step 2: Solve for total money \( y \)

Multiply both sides by \( \frac{9}{2} \): \( y = 60\times\frac{9}{2}=270 \).

Answer:

\$80

Problem 4a