Question

The owner of a small business wants to buy office equipment that will cost $950. She puts down 30 percent as a down payment. After the down payment, she is expected to pay for the rest of the equipment in Tie equal installments. If she has paid $399 in installments, how many installments have yet to be paid?

Answer 1

ANSWER:

2 installments

STEP-BY-STEP EXPLANATION:

In order to determine the answer, we must calculate the value that will be paid in installments, which is equal to the subtraction between the total value and the initial payment.

Just like that:

$\begin{gathered} i=950-950\cdot30\% \\ \\ i=950-950\cdot0.30 \\ \\ i=950-285 \\ \\ i=665 \end{gathered}$

To calculate the number of equal installments we must determine the greatest common divisor between 399 and 665, like this:

$\begin{gathered} 399=3\cdot7\cdot19 \\ \\ 665=5\cdot7\cdot19 \\ \\ \text{ The gcd is:} \\ \\ 7\cdot9=133 \\ \end{gathered}$

In other words, each installment was $133, so far he has paid 399, that is, 3 installments (399/133), we calculate the number of remaining installments as follows:

$\frac{665-399}{133}=\frac{266}{133}=2$

It means that you are missing 2 installments to pay