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Algebra / Systems of two linear equations in two variables Difficulty: Hard

In August, a car dealer completed $15$ more than $3$ times the number of sales the car dealer completed in September. In August and September, the car dealer completed $363$ sales. How many sales did the car dealer complete in September?

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Explanation

The correct answer is $87$ . It’s given that in August, the car dealer completed $15$ more than $3$ times the number of sales the car dealer completed in September. Let $x$ represent the number of sales the car dealer completed in September. It follows that $3 x plus 15$ represents the number of sales the car dealer completed in August. It’s also given that in August and September, the car dealer completed $363$ sales. It follows that $x + (3 x + 15) = 363$ , or $4 x + 15 = 363$ . Subtracting $15$ from each side of this equation yields $4 x equals 348$ . Dividing each side of this equation by $4$ yields $x equals 87$ . Therefore, the car dealer completed $87$ sales in September.