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Tobias brought some money out for shopping to prepare for his backpack travelling this December. He spent 3/7 of his money on a backpack and 2/3 of the remaining amount of money on 3 identical purification bottles. He spent the rest of his money on 3 travel first aid kits. The cost of a purification bottle is $14.80 more than the cost of each first aid kit. How much money did Tobias spend on the backpack and purification bottles altogether?

 Aug 3, 2023
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Call the total amount of money that he has at first =  M

The backpack costs (3/7)M

The amount that remains = (4/7)M

(2/3)  of this =  (2/3)(4/7)M  = (8/21)M = money spent on purification bottles

Money spent of first aid kits = (M - 3/7 M - 8/21 M ) =   (4/21)M

 

Note that  the total difference between the cost of the purification bottles and the first aid  kits = 3 (14.80)

 

So

(8/21)M - (4/21) M = 3 (14.80)

(4/21)M = 44.40

M = 44.4 *(21/4)  ≈ $233.10

 

Amt spent on backpack ≈  (3/7)(233.10) ≈ $99.90

 

Amt spent on purification bottles = (8/21)(233.10) ≈ $88.80

 

 

cool cool cool

 Aug 3, 2023

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