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Jesse and Adam are both selling items to raise money for Baseball uniforms. They are each selling
two items: chocolate bars and candles. Jesse sells 12 chocolate bars and 7 candles and makes a
total of $94. Adam sells 24 chocolate bars and 5 candles and makes a total of $98. How much does
one chocolate bar and one candle cost?
What is the system of equations that describes the problem below?
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Let solve it mentally, without using equations.
With my magic lantern, I will show the way to you.
12 chocolate bars and 7 candles cost 94 dollars. (1) hence, doubling it, we see that
24 chocolate bars and 14 candles cost 188 dollars. (2)
We also know, from the other condition, that
24 chocolate bars and 5 candles cost 98 dollars. (3)
The difference between (2) and (3) is 9 candles and/or 90 dollars.
Hence, each candle's price is 90/9 = 10 dollars.
Then from (1), 12 chocolate bars cost 94-7*10 = 24 dollars; hence, each chocolate bar's price is 24/12 = 2 dollars.
ANSWER. 2 dollars per chocolate bar and 10 dollars per each candle.
Solved // mentally.