i dont understand the way you calculated the interest, do you mind if u could explain?

Ok, let me explain

The sofa is purchased at a price of x. All my prices here are quoted in dollars.

The man pays a downpayment (initial sum) of 25% of the cost price, which is 0.25x.

For the remaining unpaid sum of 0.75x, interest will be gained on the remaining sum.

The formula for the interest earned by simple interest is given by

Interest
= Principal sum x Rate (per annum, in percent) x Duration (in years)

(In your textbook or school notes, this is denoted as I = PRT/100 where R and /100 represents the percentage rate per annum)

You can start the question from the starting to the end, or work backwards like I did. Let me explain further.

Suppose you were to start from the front.

The cost of the sofa is x. You need to pay an initial sum of 25% of the cost of the sofa, or 0.25x.

The remaining 0.75x will gain simple interest at a rate of 12% per annum for 30 months, or 2.5 years (since 30/12 = 2.5).

Interest accrued on the 0.75x outstanding
= Principal sum x interest rate in percent x duration in years
= 0.75x times 12% times 2.5 years
= 0.225x

Total sum to be paid after considering the interest
= Unpaid sum + Interest accrued
= 0.75x + 0.225x
= 0.975x

Because the person chose to pay by instalments, the total sum he has to pay in total for the instalments (over 30 months) will be 0.975x instead of the initial unpaid 0.75x.

Since he will be paying $52 a month for 30 months, he will have to pay a total of $1560 in instalments altogether.

So, 0.975x = 1560
x = 1560 / 0.975 = 1600

now i know how to do this question with ur detailed explanation!! thank you so muchhh :))