A florist makes small bouquets that use 5 roses each and... | SAT Linear equations in two variables Question, Answer Explained

Question bank / Linear equations in two variables

Math · AlgebraEasy

A florist makes small bouquets that use $5$ roses each and large bouquets that use $12$ roses each. She used a total of $156$ roses to make $x$ small bouquets and $y$ large bouquets. Which equation represents this situation?

$5x + 12y = 156$

$12x + 5y = 156$

$17(x + y) = 156$

$x + y = 156$

Show answer and explanation

Answer: A

The small bouquets use $5x$ roses and the large bouquets use $12y$ roses. Together they use $156$ roses, so $5x + 12y = 156$ .

Choice B switches the number of roses in each size of bouquet.

Why the other choices are wrong

B. This gives each small bouquet 12 roses and each large bouquet 5, which reverses the sizes.
C. This counts 17 roses in every bouquet, as if each bouquet were both small and large.
D. This sets the number of bouquets equal to 156, but 156 is the number of roses.

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