Let's carefully analyze the steps Carina took and identify any possible errors.
1. The total amount spent is [tex]$5.27, the pineapple costs $[/tex]3.40, and the cost of tomatoes per pound is $0.85. Carina correctly set up the initial equation representing the total amount spent:
[tex]\[
3.40 + 0.85x = 5.27
\][/tex]
2. To isolate [tex]\(x\)[/tex], Carina subtracted the cost of the pineapple from the total amount:
[tex]\[
0.85x = 5.27 - 3.40
\][/tex]
Let's compute the difference:
[tex]\[
5.27 - 3.40 = 1.87
\][/tex]
Therefore, the equation should now be:
[tex]\[
0.85x = 1.87
\][/tex]
3. To find the number of pounds of tomatoes, Carina should have divided 1.87 by 0.85:
[tex]\[
x = \frac{1.87}{0.85}
\][/tex]
When calculated, this yields:
[tex]\[
x \approx 2.20 \text{ pounds}
\][/tex]
Now let's check Carina's steps and identify where the error occurred:
- Carina’s second step in her solution states:
[tex]\[
0.85x = 8.67
\][/tex]
This is incorrect. Instead of 8.67, the correct simplified equation is:
[tex]\[
0.85x = 1.87
\][/tex]
So where did Carina go wrong?
- Carina made an error in the step where she simplified the equation. The correct simplification should be:
[tex]\[
0.85x = 1.87
\][/tex]
Not:
[tex]\[
0.85x = 8.67
\][/tex]
In conclusion, Carina should have subtracted 3.40 from 5.27 to get 1.87, and then divided 1.87 by 0.85 to find the correct number of pounds of tomatoes. Carina initially had the right idea but executed the simplification incorrectly and used an incorrect value in her equation. Therefore, the correct answer is that "Carina should have subtracted 3.40 from 5.27."
