For every 3 chocolates that Claire buys at the regular price, she buys a fourth chocolate for 25 cents. Claire buys 12 chocolates in total for $6.15. What is the regular price of one chocolate, in cents?
CEMC Gauss (Grade 7), 2013
Pick one
Solution
For every 3 chocolates that Claire buys at the regular price, she buys a fourth for 25 cents.
Consider dividing the 12 chocolates that Claire buys into 3 groups of 4 chocolates.
In each group of 4, Claire buys 3 chocolates at the regular price and the fourth chocolate is purchased for 25 cents.
That is, of the 12 chocolates that Claire buys, 3 are bought at 25 cents each while the remaining 9 are purchased at the regular price.
The total cost to purchase 3 chocolates at 25 cents each is cents.
Since Claire spent $6.15 and the total cost of the 25 cent chocolates was 75 cents, then the cost of the regular price chocolates was .
Since 9 chocolates were purchased at the regular price for a total of $5.40, then the regular price of one chocolate is or 60 cents.
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