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Question

The ratio of the number of chocolates to the number of sweetes that John bought was 2:7

The cost of a chocolate was $1.70 more than the cost of a sweet.

He paid $299.60 for the chocolates and sweets.

If the total cost of the sweets was $92.40 more than the total cost of chocolates, how many chocolates and sweets did John buy altogether?

 

Answer

I would solve the above question as follows :

chocolates : sweets
2u : 7u

1 chocolate ——- 1 sweet + 1.70
chocolates + sweets ——- 299.60
sweets ——- 299.60 – chocolates
sweets ——- chocolates + 92.40
chocolates + 92.40 ——- 299.60 – chocolates
chocolates ——- (299.60 – 92.40)/2 = 103.60
sweets ——- 299.60 – 103.60 or 103.60 + 92.40 = 196.00
196.00/7 = 28.00 (1u of sweets)
103.60/2 = 51.80 (1u of chocolates)
51.80 – 28 = 23.80
23.80/1.70 = 14
14 x 2 = 28 (number of chocolates)
14 x 7 = 98 (number of sweets)
98 + 28 = 126

Ans : 28 chocolates and 98 sweets, totalling 126.

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$299.60 – $92.40 = $207.20

Cost of the chocolates = $207.20 ÷ 2 = $103.60

Cost of the sweets = $103.60 + $92.40 = $196

He bought 2 units of chocolates and 7 units of sweets

Cost of 1 unit of chocolates = $103.60 ÷ 2 = $51.80

Cost of 1 unit of sweets = $196 ÷ 7 = $28

Difference in cost of 1 unit of chocolates and 1 unit of sweets

= $51.80 – $28 = $23.80

1 unit = $23.80 ÷ $1.70 = 14

9 units = 9 x 14 = 126 (Ans)

Hope it helps 🙂

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