A machine makes 9 -inch, 8 -inch, and 3 -inch parts. During a certain day, the number of 9 - inch parts that the machine makes is 4 times the number n of 8 -inch parts, and the number of 3 -inch parts is 15. During this day, the machine makes 100 parts total. Which equation represents this situation?

A machine makes 9 -inch, 8 -inch, and 3 -inch parts. During a certain day, the number of 9... | SAT Linear equations in one variable Practice

Context: In one day a machine makes $9$ -inch, $8$ -inch, and $3$ -inch parts: the number of $9$ -inch parts is $4$ times the number $n$ of $8$ -inch parts, there are $15$ three-inch parts, and $100$ parts in all. We need the equation that represents this.

Answer: D) $5n + 15 = 100$

Why: The three counts are $4n$ (9-inch), $n$ (8-inch), and $15$ (3-inch), and counts must total $100$ : $4n + n + 15 = 100$ , which simplifies to $5n + 15 = 100$ .

Traps:

A) $9(4n) + 8n + 3(15) = 100$ — multiplies each count by its length, so the left side totals inches; but $100$ counts parts, not inches.
B) $9n + 8n + 3n = 100$ — uses the lengths as coefficients and gives every size the same count $n$ , ignoring both the " $4$ times" relation and the fixed $15$ .
C) $4n + 15 = 100$ — leaves the $n$ eight-inch parts out of the total.

Question Bank

Question Bank

SAT Linear equations in one variable practice question

Explanation