Subject Test Math 1

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Subject Test Math 1

Question 2 of 32

A band wants to distribute its music on compact discs (CDs). The equipment to produce the CDs costs $$ 250$ , and blank CDs cost $$ 5.90$ for a package of $10$ . Which of the following represents the total cost, in dollars, to produce $n$ CDs, where $n$ is a multiple of $10$ ?

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$left parenthesis 250 plus 0.59 right parenthesis n$

Correct Answer:

No

$250 invisible times plus text end text 0.59 n$

Correct Answer:

Yes

$left parenthesis 250 invisible times plus 5.90 right parenthesis n$

Correct Answer:

No

$250 invisible times plus 5.90 n$

Correct Answer:

No

$250 n plus 5.90$

Correct Answer:

No

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The correct answer is B.

The cost of the equipment is $$ 250$ , and each package of $10$ blank CDs costs $$ 5.90$ . The total cost for the band to produce $10$ CDs, that is, $1$ package, is $250 + 5.90 = 255.90$ dollars, and the total cost to produce $20$ CDs, that is, $2$ packages, is $250 + 5.90 (2) = 250 + 11.80 = 261.80$ dollars.

One way to determine the correct expression is to find the slope-intercept form of the equation of the line that passes through the two points given by the ordered pairs $(10, 255.90)$ and $(20, 261.80)$ . The line has slope $\frac{261.80 - 255.90}{20 - 10} = 0.59$ and $y$ -intercept $250$ , which is the cost, in dollars, for the band to produce $0$ CDs after purchasing the equipment. The equation of this line is $y = 0.59 n + 250$ , where $n$ is the number of CDs used.

Alternatively, note that the total cost to produce $10$ CDs is $250 + 5.90 = 250 + 0.59 (10)$ dollars, and the cost to produce $20$ CDs is $250 + 5.90 (2) = 250 + 0.59 (20)$ dollars, so, in general, if $n$ is a multiple of $10$ , then the total cost to produce $n$ CDs is $250 + 5.90 (\frac{n}{10}) = 250 + 0.59 n$ dollars.

Question Difficulty:

easy

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Subject Test Math 1

Question 2 of 32

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