Question

Rama was getting some items for the new school year. First, he bought some textbooks with $8 more than 1/3 of his money. Next, Next, he bought his stationery with $12.20 less than 1/2 of his remaining money. Lastly, he bought some school socks with $2.80 more than 1/2 of the money left. Then, he had $15.40 with him. How

much money did he have at first?

Answer 1

$84.60

Explanation:

You want to know the money Rama started with given a series of expenditures that resulted in $15.40 remaining.

Setup

Let x represent the amount of money Rama started with.

After his first purchase, the amount remaining was ...

a = x - (8+1/3x)

After his second purchase, the amount remaining was ...

b = a -(1/2a -12.20)

After his last purchase, the amount remaining was ...

c = b -(2.80 +1/2b)

Solution

Expanding each of these relations and writing in terms of x, we have ...

a = x - 8 - 1/3x = 2/3x -8

b = a -1/2a +12.20 = 1/2(2/3x -8) +12.20 = 1/3x -4 +12.20 = 1/3x +8.20

c = b - 2.80 -1/2b = 1/2b -2.80 = 1/2(1/3x +8.20) -2.80 = 1/6x +4.10 -2.80

c = 1/6x +1.30

This amount remaining is 15.40, so we have ...

1/6x +1.30 = 15.40

1/6x = 14.10

x = 84.60

Rama has $84.60 at first.

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Additional comment

We can check this by working through the original list of expenditures.

$8 more than 1/3 of $84.60 is $36.20, so $48.40 remained.

$12.20 less than 1/2 of $48.40 is $12.00, so $36.40 remained.

$2.80 more than 1/2 of $36.40 is $21.00, so $15.40 remained.

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