Question

diep is saving money so he can buy a used car in 12 months. the total cost of the car he wants is $1,450. diep determines that he needs to save $120 each month to be able to afford the car, as shown below.

\\(12 \overline{) 1450}\\)

what error did diep make?

there is a subtraction error. diep will need to save less than $120 each month.
there is a subtraction error. diep will need to save exactly $121 each month.
there is a multiplication error. diep needs to save exactly $120.83 each month.
there is a multiplication error. diep needs to save an average of \\(\\$120.8\overline{3}\\) each month. some months he needs to save \\(\\$120.83\\) and other months he needs to save \\(\\$120.84\\).

Explanation:

Analyze the given long division work

Using the Long Division Steps knowledge point

$$
LATEXBLOCK0
$$

Identify the type of error

The error occurs in the multiplication step of the division process. Diep calculated \(12 \times 2\) as \(25\) instead of \(24\). This is a multiplication error.

Calculate the correct monthly savings

To find the exact amount Diep needs to save each month:

$$ \frac{1450}{12} = 120.8333\dots = 120.8\bar{3} $$

Thus, Diep needs to save an average of \(\$120.8\bar{3}\) each month.

Match with the correct option

The fourth option states: "There is a multiplication error. Diep needs to save an average of \(\$120.8\bar{3}\) each month. Some months he needs to save \(\$120.83\) and other months he needs to save \(\$120.84\)." This matches our analysis.

Answer:

• There is a subtraction error. Diep will need to save less than $120 each month.
• There is a subtraction error. Diep will need to save exactly $121 each month.
• There is a multiplication error. Diep needs to save exactly $120.83 each month.
• There is a multiplication error. Diep needs to save an average of $120.83̄ each month. Some months he needs to save $120.83 and other months he needs to save $120.84. (Correct answer)