Writing and solving equations can be helpful for solving real-world situations where you need to find an unknown number.

Question

Melissa gets $2 more a week in allowance than 2 times her friend Monica’s allowance. If Melissa gets $20 in allowance each week, how much does Monica get?
Christina charges a flat fee of $10 plus $3 per child when she babysits for an hour. How many children did Christina babysit if she made $16 an hour?
There are 27 basketball teams in the Storyville Park District. This is 5 less than 2 times the number of teams in the Friendly Village Park District. How many basketball teams are in the Friendly Village Park District?
You go to a concert and purchase 4 identical t-shirts and 1 poster. The poster costs $14 and you spend $98 in all. How much did 1 t-shirt cost?
Talya is saving money to buy a new video game system that costs $360. She has already saved $72 and is planning on saving an additional $24 per week.
Write an expression to represent the amount of money saved after x weeks. Then use your expression to complete the following table.
Number of Weeks Amount of Savings ($)
1 96
2 ?
3 ?
4 ?
Write and solve an equation to find the number of weeks it will take Tayla to save the $360.

Answer 1

Let's solve each problem step by step.

Problem 1: Melissa and Monica's Allowance

The equation is based on the statement: "Melissa gets $2 more a week in allowance than 2 times her friend Monica’s allowance."

Let \( m \) be Monica's allowance. According to the problem: \[ 2m + 2 = 20 \]

Now, let's solve for \( m \):

1. Subtract 2 from both sides: \[ 2m = 18 \]
2. Divide by 2: \[ m = 9 \]

Monica gets $9 in allowance each week.

Problem 2: Christina's Babysitting Earnings

The total amount Christina earns is given by: \[ \text{Total Earnings} = 10 + 3c \] where \( c \) is the number of children she babysits.

We know her total earnings for the hour is $16, so: \[ 10 + 3c = 16 \]

Now, let's solve for \( c \):

1. Subtract 10 from both sides: \[ 3c = 6 \]
2. Divide by 3: \[ c = 2 \]

Christina babysat 2 children.

Problem 3: Basketball Teams in Friendly Village

Let \( x \) be the number of teams in the Friendly Village Park District. According to the problem: \[ 2x - 5 = 27 \]

Now, let's solve for \( x \):

1. Add 5 to both sides: \[ 2x = 32 \]
2. Divide by 2: \[ x = 16 \]

There are 16 basketball teams in the Friendly Village Park District.

Problem 4: T-shirt and Poster Costs

Let \( p \) be the cost of one t-shirt. The total cost for 4 t-shirts and 1 poster is: \[ 4p + 14 = 98 \]

Now, let's solve for \( p \):

1. Subtract 14 from both sides: \[ 4p = 84 \]
2. Divide by 4: \[ p = 21 \]

Each t-shirt costs $21.

Problem 5: Talya's Savings for a Video Game System

The expression to represent the amount of money saved after \( x \) weeks is: \[ \text{Amount Saved} = 72 + 24x \]

We can now complete the table based on this expression:

• Number of Weeks 1: \[ 72 + 24(1) = 96 \]
• Number of Weeks 2: \[ 72 + 24(2) = 120 \]
• Number of Weeks 3: \[ 72 + 24(3) = 144 \]
• Number of Weeks 4: \[ 72 + 24(4) = 168 \]

| Number of Weeks | Amount of Savings ($) | |------------------|-----------------------| | 1 | 96 | | 2 | 120 | | 3 | 144 | | 4 | 168 |

Now, to find the number of weeks it will take Talya to save $360: Set the equation: \[ 72 + 24x = 360 \]

Now, solve for \( x \):

1. Subtract 72 from both sides: \[ 24x = 288 \]
2. Divide by 24: \[ x = 12 \]

It will take Talya 12 weeks to save $360.