Danny spent 3/8 of his money on a dining table set, 1/4 of it on a cabinet and 1/3 of the remainder on a television and a study table. The cost of the television was $1 200, which was thrice the cost of the study table. How much did Danny pay for the dining table set?

Guest Aug 22, 2022

#1**0 **

Let the total amount of money==M

M - 3/8M - 1/4M ==3/8M - balance

1/3 x 3/8M ==1/8M - he spent on TV

1/8M ==1,200

M ==1,200 x 8==$9,600 - total sum of his money.

1,200 / 3 ==$400 - cost of the study table.

9,600 x 1/4 ==$2,400 - he spent on the cabinet

**9,600 x 3/8 ==$3,600 - he spent on the dining table set.**

Guest Aug 22, 2022

#2**+1 **

SORRY, I MISREAD PART OF THE QUESTION!

Let the total amount of money==M

M - 3/8M - 1/4M ==3/8M - balance

1/3 x 3/8M ==1/8M - he spent on TV AND the study table

1200 / 3 ==$400 - cost of the study table

1/8M ==1,200 + 400 ==1,600

M ==1,600 x 8 ==$12,800 - total amount of money

**12,800 x 3/8 ==$4,800 - he spent on the dining table set.**

Guest Aug 22, 2022

#3**+3 **

Cost of TV = 1200

Cost of study table = 1200 / 3 = 400

Cost of TV and study table = 1600

Let A be the total amount of money that he had

What he has left BEFORE buying the TV and dining table =

A - (3/8)A - (1/4)A =

(8/8)A - (3/8)A - (2/8)A =

(8 - 3 - 2) / 8 * A =

(3/8)A

And he spends (1/3) of this on the TV set and study table

So (1/3)(3/8)A = (1/8)A

And this must be what he has left to spend on the TV and the study table

So

(1/8)A = 1200 + 400

(1/8)A = 1600

The total amount of money he has to spend = 8 * 1600 = 12800

But he spends (3/8)A = (three times 1600) on the dining table = $4800

Proof

He starts with 12800

He spends (3/8) of this on the dining table = 4800

He spends (1/4) on the cabinet = 3200

What he has left after these two purchases = 12800 - 4800 - 3200 = 4800

He spends (1/3) of this on the TV and study table = 1600

CPhill Aug 22, 2022