Sam is helping his brother Jason do carpentry and general repair jobs. Jason gave Sam some money for supplies. Sam bought some tools for $20.80, then spent one

Question

Sam is helping his brother Jason do carpentry and general repair jobs. Jason gave Sam some money for supplies. Sam bought some tools for $20.80, then spent one half of what was left for wood. He spent one third of what was left after that on paint and one third on buckets and brushes, and he returned with $13.20. How much money did Jason give Sam?

 

Answer 1

working backwards:

$13.20 was spent on paint

$13.20 was spent on buckets and brushes

$13.20 remains

This subtotal is $39.60, so he spent 39.60 on wood.

THe subtotal is now 79.20

Adding 20.80 for the tools gives a starting total of 100

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Algebraic solution:

Begins with X

spent 20.80 on tools, so X-20.80 remains

half of that was spent on wood, so (1/2)(x - 20.80)

was spent on wood, which is (1/2)x - 10.40, and

(1/2)x - 10.40 remains

1/3 of that is 13.20, and also 1/3 of that was spent

on paint, and the last 1/3 of it spent on brushes and buckets.

so 1/3 [ (1/2)x - 10.40 ] = 13.20

Multiplying by 3:

(1/2)x - 10.40 = 39.60

Adds 10.40:

(1/2)x = 50

Multiplies by 2

x = 100

Starts with 100...

20.80 spent on tools.... 79.20 remains

half of that spent on wood, so 39.60 spent on wood

and 39.60 remains

1/3 of that is in fact 13.20