A coffee shop sells small coffees for 3.50 each and large... | SAT Systems of two linear equations in two variables Question, Answer Explained

Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

A coffee shop sells small coffees for $\$3.50$ each and large coffees for $\$4.25$ each. One morning it sold $120$ coffees for a total of $\$462$ . How many large coffees did it sell that morning?

$42$

$56$

$64$

$132$

Show answer and explanation

Answer: B

Let $S$ be the number of small coffees and $L$ the number of large coffees. Then $S + L = 120$ and $3.50S + 4.25L = 462$ . Substituting $S = 120 - L$ gives $420 - 3.50L + 4.25L = 462$ , so $0.75L = 42$ and $L = 56$ .

Choice C, $64$ , is the number of small coffees.

Why the other choices are wrong

A. 42 dollars is the revenue above 120 × $3.50. Divide it by the $0.75 price difference to get the number of large coffees.
C. 64 is the number of small coffees, not large coffees.
D. This divides $462 by $3.50, as if every coffee sold were small.

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