At a fundraiser, a club sold candles for 12 each and bars of... | SAT Systems of two linear equations in two variables Question, Answer Explained

Question bank / Systems of two linear equations in two variables

Math · AlgebraEasy

At a fundraiser, a club sold candles for $\$12$ each and bars of soap for $\$5$ each. The club sold $85$ items in all and collected $\$642$ . If $c$ is the number of candles and $s$ is the number of bars of soap the club sold, which system of equations represents this situation?

A

$c + s = 642$ and $12c + 5s = 85$

B

$c + s = 85$ and $5c + 12s = 642$

C

$c + s = 85$ and $12c + 5s = 642$

D

$c + s = 85$ and $\frac{c}{12} + \frac{s}{5} = 642$

Show answer and explanation

Answer: C

The total number of items gives $c + s = 85$ . The candles bring in $12c$ dollars and the soap brings in $5s$ dollars, so $12c + 5s = 642$ .

Choice B attaches each price to the wrong item.

Why the other choices are wrong

A. This switches the totals. 85 is the number of items and 642 is the amount of money.
B. This pairs each price with the wrong item. Candles cost $12, so the candle term is 12c.
D. This divides the number of each item by its price. Money collected is the number sold times the price.

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