Answer :
Sure! Let's break down the problem into two parts step-by-step:
### Part (a)
You want to buy a pet iguana that costs \[tex]$48. You currently have \$[/tex]12 and plan to save \[tex]$9 per week. We need to set up an equation to determine how many weeks it will take to afford the iguana.
1. Define the variable:
- Let \( w \) represent the number of weeks needed to save enough money.
2. Set up the equation:
- The total amount of money you will have after \( w \) weeks can be represented by:
\[
9w + 12
\]
- This must equal the cost of the iguana, which is \$[/tex]48:
[tex]\[
9w + 12 = 48
\][/tex]
3. Solve the equation:
- Subtract 12 from both sides to isolate the term with [tex]\( w \)[/tex] on one side:
[tex]\[
9w + 12 - 12 = 48 - 12
\][/tex]
[tex]\[
9w = 36
\][/tex]
- Divide both sides by 9 to solve for [tex]\( w \)[/tex]:
[tex]\[
w = \frac{36}{9}
\][/tex]
[tex]\[
w = 4
\][/tex]
So, it will take 4 weeks to save enough money to buy the iguana.
### Part (b)
Now, let's find out how much money you should save each week if you want to buy the iguana in 6 weeks.
1. Set up the equation for 6 weeks:
- Let [tex]\( s \)[/tex] represent the amount of money to save each week.
2. Determine the total amount needed after 6 weeks:
- We need enough money to buy the iguana, so:
[tex]\[
6s + 12 = 48
\][/tex]
3. Solve the equation:
- Subtract 12 from both sides to isolate the term with [tex]\( s \)[/tex] on one side:
[tex]\[
6s + 12 - 12 = 48 - 12
\][/tex]
[tex]\[
6s = 36
\][/tex]
- Divide both sides by 6 to solve for [tex]\( s \)[/tex]:
[tex]\[
s = \frac{36}{6}
\][/tex]
[tex]\[
s = 6
\][/tex]
So, you should save \[tex]$6 each week to buy the iguana in 6 weeks.
### Summary
- Part (a): It will take you 4 weeks to save enough money to buy the iguana if you save \$[/tex]9 per week.
- Part (b): If you want to buy the iguana in 6 weeks, you should save \$6 each week.
### Part (a)
You want to buy a pet iguana that costs \[tex]$48. You currently have \$[/tex]12 and plan to save \[tex]$9 per week. We need to set up an equation to determine how many weeks it will take to afford the iguana.
1. Define the variable:
- Let \( w \) represent the number of weeks needed to save enough money.
2. Set up the equation:
- The total amount of money you will have after \( w \) weeks can be represented by:
\[
9w + 12
\]
- This must equal the cost of the iguana, which is \$[/tex]48:
[tex]\[
9w + 12 = 48
\][/tex]
3. Solve the equation:
- Subtract 12 from both sides to isolate the term with [tex]\( w \)[/tex] on one side:
[tex]\[
9w + 12 - 12 = 48 - 12
\][/tex]
[tex]\[
9w = 36
\][/tex]
- Divide both sides by 9 to solve for [tex]\( w \)[/tex]:
[tex]\[
w = \frac{36}{9}
\][/tex]
[tex]\[
w = 4
\][/tex]
So, it will take 4 weeks to save enough money to buy the iguana.
### Part (b)
Now, let's find out how much money you should save each week if you want to buy the iguana in 6 weeks.
1. Set up the equation for 6 weeks:
- Let [tex]\( s \)[/tex] represent the amount of money to save each week.
2. Determine the total amount needed after 6 weeks:
- We need enough money to buy the iguana, so:
[tex]\[
6s + 12 = 48
\][/tex]
3. Solve the equation:
- Subtract 12 from both sides to isolate the term with [tex]\( s \)[/tex] on one side:
[tex]\[
6s + 12 - 12 = 48 - 12
\][/tex]
[tex]\[
6s = 36
\][/tex]
- Divide both sides by 6 to solve for [tex]\( s \)[/tex]:
[tex]\[
s = \frac{36}{6}
\][/tex]
[tex]\[
s = 6
\][/tex]
So, you should save \[tex]$6 each week to buy the iguana in 6 weeks.
### Summary
- Part (a): It will take you 4 weeks to save enough money to buy the iguana if you save \$[/tex]9 per week.
- Part (b): If you want to buy the iguana in 6 weeks, you should save \$6 each week.
