Question

algebra 1 unit 2a: equations & inequalities notes

1. you and three friends divide the proceeds of a garage sale equally. the garage sale earned $412. how much money did each friend receive?

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1. on her ipod, mia has rock songs and dance songs. she currently has 14 rock songs. she has 48 songs in all. how many dance songs does she have?

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1. brianna has saved $600 to buy a new tv. if the tv she wants costs $1800 and she saves $20 a week, how many months will it take her to buy the tv (4 weeks = 1 month)?

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1. it costs raquel $5 in tolls to drive to work and back each day, plus she uses 3 gallons of gas. it costs her a total of $15.50 to drive to work and back each day. how much per gallon is raquel paying for her gas?

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1. a rectangle is 12m longer than it is wide. its perimeter is 68m. find its length and width (hint: p = 2w + 2l).

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Explanation:

2.

Step1: Define the number of people

There are you and 3 friends, so 4 people in total. Let $x$ be the amount of money each person receives.

Step2: Set up the equation

The total money from the garage - sale is $412$. So the equation is $4x = 412$.

Step3: Solve for $x$

Divide both sides of the equation by 4: $x=\frac{412}{4}=103$.

Step1: Define the variables

Let $d$ be the number of dance - songs. We know the number of rock songs is 14 and the total number of songs is 48.

Step2: Set up the equation

The sum of rock songs and dance songs is the total number of songs. So the equation is $14 + d=48$.

Step3: Solve for $d$

Subtract 14 from both sides of the equation: $d = 48 - 14=34$.

Step1: Define the variables

Let $m$ be the number of months. She saves $20$ per week, so she saves $20\times4 = 80$ per month. She already has 600 and the TV costs 1800.

Step2: Set up the equation

The money she has plus the money she will save in $m$ months is equal to the cost of the TV. So the equation is $600+80m = 1800$.

Step3: Solve for $m$

First, subtract 600 from both sides: $80m=1800 - 600 = 1200$. Then divide both sides by 80: $m=\frac{1200}{80}=15$.

Answer:

Variables: $x$ (amount of money each person receives)
Equation: $4x = 412$
Each friend receives $103$.

3.