Answer :
Sure! Let's break down the problem step-by-step to find out how many lawns Kevin needs to mow to earn enough money to buy the bike he wants.
1. Understand the Problem:
- Kevin wants to buy a bike that costs \[tex]$175.
- He makes \$[/tex]15 for each lawn that he mows.
- He already has some initial amount of money that we'll assume is \[tex]$65 based on the context.
2. Set Up the Equation:
Let's denote the number of lawns Kevin needs to mow by \( x \).
The total amount of money Kevin will have after mowing \( x \) lawns can be calculated by the formula:
\[
\text{Total money} = \text{Initial money} + (\text{money per lawn} \times \text{number of lawns})
\]
Given the values:
\[
\text{Total money} = 65 + 15x
\]
3. Form the Inequality:
We want the total amount of money to be at least \$[/tex]175.
[tex]\[
65 + 15x \geq 175
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find the minimum number of lawns Kevin needs to mow, we need to isolate [tex]\( x \)[/tex]:
[tex]\[
65 + 15x \geq 175
\][/tex]
Subtract 65 from both sides:
[tex]\[
15x \geq 110
\][/tex]
Divide both sides by 15:
[tex]\[
x \geq \frac{110}{15}
\][/tex]
Calculating the right-hand side gives:
[tex]\[
x \geq 7.33
\][/tex]
5. Round Up the Result:
Since Kevin can only mow a whole number of lawns, we round up to the next whole number. Therefore, Kevin needs to mow at least 8 lawns to have enough money to buy the bike.
So, Kevin needs to mow 8 lawns to earn enough money to buy the bike.
1. Understand the Problem:
- Kevin wants to buy a bike that costs \[tex]$175.
- He makes \$[/tex]15 for each lawn that he mows.
- He already has some initial amount of money that we'll assume is \[tex]$65 based on the context.
2. Set Up the Equation:
Let's denote the number of lawns Kevin needs to mow by \( x \).
The total amount of money Kevin will have after mowing \( x \) lawns can be calculated by the formula:
\[
\text{Total money} = \text{Initial money} + (\text{money per lawn} \times \text{number of lawns})
\]
Given the values:
\[
\text{Total money} = 65 + 15x
\]
3. Form the Inequality:
We want the total amount of money to be at least \$[/tex]175.
[tex]\[
65 + 15x \geq 175
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
To find the minimum number of lawns Kevin needs to mow, we need to isolate [tex]\( x \)[/tex]:
[tex]\[
65 + 15x \geq 175
\][/tex]
Subtract 65 from both sides:
[tex]\[
15x \geq 110
\][/tex]
Divide both sides by 15:
[tex]\[
x \geq \frac{110}{15}
\][/tex]
Calculating the right-hand side gives:
[tex]\[
x \geq 7.33
\][/tex]
5. Round Up the Result:
Since Kevin can only mow a whole number of lawns, we round up to the next whole number. Therefore, Kevin needs to mow at least 8 lawns to have enough money to buy the bike.
So, Kevin needs to mow 8 lawns to earn enough money to buy the bike.
