Question

1. $\frac{2}{3}$ of your birthday cake was eaten at the party. you eat $\frac{1}{2}$ of what’s left the next day. what fraction of the cake is now remaining?
2. a recipe for gumbo needs 2 pounds of chicken to feed 6 people.

a. how much chicken do you need to feed 12 people?
b. how much do you need to feed 15 people?
c. how many people can you feed with a gumbo that uses $4\frac{1}{3}$ pounds of chicken?

1. the federal government taxes your paycheck 12 percent. this means $\frac{12}{100}$ of the money you earn is taken by the government. in other words, for every $100 you make, you must pay $12 in taxes.

a. how much do you pay in taxes if you earn $30,000?
b. how much do you pay in taxes if you earn $28,500?
c. if you pay $3600 in taxes, how much money did you earn before you were taxed?

Explanation:

Step1: Find remaining cake after party

$1 - \frac{2}{3} = \frac{1}{3}$

Step2: Eat half the leftover cake

$\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

Step3: Calculate final remaining cake

$\frac{1}{3} - \frac{1}{6} = \frac{2}{6} - \frac{1}{6} = \frac{1}{6}$

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Step1: Find chicken per person

$\frac{2}{6} = \frac{1}{3}$ pounds per person

Step2a: Chicken for 12 people

$12 \times \frac{1}{3} = 4$

Step2b: Chicken for 15 people

$15 \times \frac{1}{3} =5$

Step2c: Number of people for $4\frac{1}{3}$ lbs

$4\frac{1}{3} = \frac{13}{3}$, $\frac{13/3}{1/3}=13$

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Step3a: 12% of $30,000$

$0.12 \times 30000 = 3600$

Step3b: 12% of $28,500$

$0.12 \times 28500 = 3420$

Step3c: Pre-tax income from $3600$ taxes

$\frac{3600}{0.12}=30000$

Answer:

1. $\boldsymbol{\frac{1}{6}}$
2. a. $\boldsymbol{4}$ pounds

b. $\boldsymbol{5}$ pounds
c. $\boldsymbol{13}$ people

1. a. $\boldsymbol{\$3600}$

b. $\boldsymbol{\$3420}$
c. $\boldsymbol{\$30,000}$