Carina spent a total of [tex]$5.27 buying a pineapple for $[/tex]3.40 and some tomatoes that were on sale for $0.85 per pound. To determine the number of pounds of tomatoes that she bought, [tex]\( x \)[/tex], Carina wrote and solved the equation as shown below:

[tex]\[
\begin{aligned}
3.40 + 0.85x & = 5.27 \\
0.85x & = 1.87 \\
x & = 2.2 \text{ pounds}
\end{aligned}
\][/tex]

Where, if anywhere, did Carina make an error?

A. Carina did not make any errors.
B. The initial equation that Carina wrote was incorrect.
C. Carina should have subtracted 3.40 from 5.27.
D. Carina should have divided 1.87 by 0.85.



Answer :

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.