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Subject Test Math 1

Question 2 of 32

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SAT Subject Test

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

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 plus 5.90 invisible times equals 255.90 dollars, and the total cost to produce 20 CDs, that is, 2 packages, is 250 plus 5.90 left parenthesis 2 right parenthesis equals 250 plus 11.80 equals 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 left parenthesis 10 comma 255.90 right parenthesis and left parenthesis 20 comma 261.80 right parenthesis. The line has slope fraction numerator 261.80 invisible times minus 255.90 over denominator 20 minus 10 end fraction equals 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 equals 0.59 n plus 250, where n is the number of CDs used.

Alternatively, note that the total cost to produce 10 CDs is 250 plus 5.90 equals 250 plus 0.59 left parenthesis 10 right parenthesis dollars, and the cost to produce 20 CDs is 250 plus 5.90 left parenthesis 2 right parenthesis equals 250 plus 0.59 left parenthesis 20 right parenthesis dollars, so, in general, if n is a multiple of 10, then the total cost to produce n CDs is 250 invisible times plus 5.90 left parenthesis fraction numerator n over denominator 10 end fraction right parenthesis equals 250 plus 0.59 n dollars.

Question Difficulty: 
easy