M:C:MC:14

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The toll rates for crossing a bridge are $6.50 for a car and $10 for a truck. During a two-hour period, a total of 187 cars and trucks crossed the bridge, and the total collected in tolls was $1,338. Solving which of the following systems of equations yields the number of cars, x, and the number of trucks, y, that crossed the bridge during the two hours?

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$table attributes columnalign right center left columnspacing 2px end attributes row cell x plus y end cell equals cell 1 comma 338 end cell row cell 6.5 x plus 10 y end cell equals 187 end table$

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$table attributes columnalign right center left columnspacing 2px end attributes row cell x plus y end cell equals 187 row cell 6.5 x plus 10 y end cell equals cell fraction numerator 1 comma 338 over denominator 2 end fraction end cell end table$

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$table attributes columnalign right center left columnspacing 2px end attributes row cell x plus y end cell equals 187 row cell 6.5 x plus 10 y end cell equals cell 1 comma 338 end cell end table$

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Yes

$table attributes columnalign right center left columnspacing 2px end attributes row cell x plus y end cell equals 187 row cell 6.5 x plus 10 y end cell equals cell 1 comma 338 cross times 2 end cell end table$

Correct Answer:

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Choice C is correct. If x is the number of cars that crossed the bridge during the two hours and y is the number of trucks that crossed the bridge during the two hours, then $x space plus space y$ represents the total number of cars and trucks that crossed the bridge during the two hours, and $6.5 x space plus space 10 y$ represents the total amount collected in the two hours. Therefore, the correct system of equations is $x space plus thin space y space equals space 187$ and $6.5 x space plus space 10 y space equals space 1 comma 338.$

Choice A is not the correct answer. The student may have mismatched the symbolic expressions for total cars and trucks and total tolls collected with the two numerical values given. The expression $x space plus space y$ represents the total number of cars and trucks that crossed the bridge, which is 187.

Choice B is not the correct answer. The student may have attempted to use the information that the counts of cars, trucks, and tolls were taken over a period of two hours, but this information is not needed in setting up the correct system of equations. The expression $6.5 x space plus space 10 y$ represents the total amount of tolls collected, which is $1,338, not $fraction numerator text $ end text 1 comma 338 over denominator 2 end fraction.$

Choice D is not the correct answer. The student may have attempted to use the information that the counts of cars, trucks, and tolls were taken over a period of two hours, but this information is not needed in setting up the correct system of equations. The expression $6.5 x space plus space 10 y$ represents the total amount of tolls collected, which is $1,338 not $text $ end text 1 comma 338 cross times 2.$

Question Difficulty:

medium

Objective:

Students must create a system of linear equations to represent a real-world situation.

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Question 18 of 30

M:C:MC:14

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