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# Fractions

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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?

Aug 22, 2022

#1
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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.

Aug 22, 2022
#2
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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
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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   Aug 22, 2022