Question
Writing and solving equations can be helpful for solving real-world situations where you need to find an unknown number.
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.
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.
Answers
GPT-4o mini
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.**
### 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.**