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?
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.
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.
+128460 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
