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Linear equations in two variables SAT question

Math · Algebra · Easy · Answer it here, explanation included.

Davio bought some potatoes and celery. The potatoes cost $$0.69$ per pound, and the celery cost $$0.99$ per pound. If Davio spent $$5.34$ in total and bought twice as many pounds of celery as pounds of potatoes, how many pounds of celery did Davio buy?

ExplanationShow

Choice D is correct. Let $p$ represent the number of pounds of potatoes and let $c$ represent the number of pounds of celery that Davio bought. It’s given that potatoes cost $$0.69$ per pound and celery costs $$0.99$ per pound. If Davio spent $$5.34$ in total, then the equation $0.69 p + 0.99 c = 5.34$ represents this situation. It’s also given that Davio bought twice as many pounds of celery as pounds of potatoes; therefore, $c = 2 p$ . Substituting $2 p$ for $c$ in the equation $0.69 p + 0.99 c = 5.34$ yields $0.69 p + 0.99 (2 p) = 5.34$ , which is equivalent to $0.69 p + 1.98 p = 5.34$ , or $2.67 p = 5.34$ . Dividing both sides of this equation by $2.67$ yields $p = 2$ . Substituting $2$ for $p$ in the equation $c = 2 p$ yields $c = 2 (2)$ , or $c = 4$ . Therefore, Davio bought $4$ pounds of celery.

Choice A is incorrect. This is the number of pounds of potatoes, not the number of pounds of celery, Davio bought.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

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Linear equations in two variables SAT question

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