Let's analyze the steps Carina took to solve the problem and identify where any possible errors might have occurred.
The problem states:
- Carina spent a total of [tex]$5.27.
- She bought a pineapple for $[/tex]3.40.
- The price of the tomatoes is [tex]$0.85 per pound.
We need to determine how many pounds of tomatoes, \( x \), Carina bought.
1. Carina's initial equation:
\[ 3.40 + 0.85x = 5.27 \]
This equation correctly represents the total cost ($[/tex]3.40 for the pineapple plus [tex]$0.85 times the number of pounds of tomatoes equals $[/tex]5.27).
2. Solving for [tex]\( x \)[/tex]:
We need to isolate [tex]\( x \)[/tex], so first we subtract the cost of the pineapple from the total cost:
[tex]\[ 3.40 + 0.85x = 5.27 \][/tex]
[tex]\[ 0.85x = 5.27 - 3.40 \][/tex]
[tex]\[ 0.85x = 1.87 \][/tex]
3. Now, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by the price per pound of tomatoes:
[tex]\[ x = \frac{1.87}{0.85} \][/tex]
Calculating this gives:
[tex]\[ x \approx 2.2 \][/tex]
So, Carina bought approximately 2.2 pounds of tomatoes.
Reviewing Carina's steps:
- Her initial setup of the equation was correct.
- She correctly subtracted the cost of the pineapple from the total.
- However, she made an error in her arithmetic when isolating [tex]\( x \)[/tex]: she wrote [tex]\( 0.85x = 8.67 \)[/tex] and [tex]\( x = 10.2 \)[/tex], which is incorrect.
The correct steps after setting up the initial equation should result in [tex]\( x \approx 2.2 \)[/tex].
Therefore, Carina's error was in the subtraction step and the final solution. Specifically, she should have subtracted [tex]\( 3.40 \)[/tex] from [tex]\( 5.27 \)[/tex] correctly and subsequently divided the correct remainder by [tex]\( 0.85 \)[/tex].
The correct conclusion is:
Carina should have subtracted [tex]$3.40 from $[/tex]5.27.
