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Modeling with Linear Systems — Quiz Answers

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1
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Miguel and Beth like to play video games together. Miguel has m video games, and Beth has b video games. Miguel has 4 more video games than Beth, and together they have a total of 24 video games. Which system of equations can be used to find how many video games belong to each friend?

A
the 2 by 1 column matrix row 1 m plus b is equal to 24 row 2 m is equal to b plus 4
B
the 2 by 1 column matrix row 1 m plus b plus 4 is equal to 24 row 2 b is equal to m plus 4
C
the 2 by 1 column matrix row 1 m plus b is equal to 24 row 2 b is equal to m plus 4
D
the 2 by 1 column matrix row 1 m plus b plus 4 is equal to 24 row 2 m is equal to b plus 4
2
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Lisa leaves a gas station and drives at an average rate of 50 mi/hr Keisha leaves the gas station one hour later and drives along the same route at an average rate of 60 mi/hr Let d represent the distance driven in miles and t represent the time since Lisa left the gas station. Which system of equations can be used to find how long after Lisa left the gas stations that she is passed by Keisha?

A
the 2 by 1 column matrix row 1 d is equal to 50 t row 2 d is equal to 60 t minus 1
B
the 2 by 1 column matrix row 1 d is equal to 50 times open paren t minus 1 close paren row 2 d is equal to 60 t
C
the 2 by 1 column matrix row 1 d is equal to 50 t row 2 d is equal to 59 t
D
the 2 by 1 column matrix row 1 d is equal to 50 t row 2 d is equal to 60 times open paren t minus 1 close paren
3

A school drama department sells 40 more student tickets than adult tickets. Charging 8 dollars for adult tickets and 6 dollars for student tickets, the drama department raises a total of 1 dollars comma 920 in ticket sales. Let x represent the number of adult tickets sold and y represent the number of student tickets sold. Which system of equations can be used to find how many of each ticket is sold?

A
the 2 by 1 column matrix row 1 x is equal to 40 plus y row 2 8 x plus 6 y is equal to 1920
B
the 2 by 1 column matrix row 1 y is equal to 40 plus x row 2 8 x plus 6 y is equal to 1920
C
the 2 by 1 column matrix row 1 y is equal to 40 minus x row 2 8 x plus 6 y is equal to 1920
D
the 2 by 1 column matrix row 1 x is equal to 40 minus y row 2 8 x plus 6 y is equal to 1920
4

The Carson family paid 192 dollars for two adult and three youth tickets to an amusement park. At the same park, the Davis family paid 148 dollars for one adult and four youth tickets. Let x represent the cost of an adult ticket, and let y represent the cost of a youth ticket. Which system of equations can be used to find the cost of each ticket?

A
the 2 by 1 column matrix row 1 5 x plus 5 y is equal to 192 row 2 5 x plus 5 y is equal to 148
B
the 2 by 1 column matrix row 1 2 x plus 3 y is equal to 192 row 2 x plus 4 y is equal to 148
C
the 2 by 1 column matrix row 1 2 x plus 3 y is equal to 192 row 2 4 x plus y is equal to 148
D
the 2 by 1 column matrix row 1 x plus y is equal to 192 row 2 x plus y is equal to 148
6

The given system of equations models the coins in a jar containing n nickels, d dimes, and q quarters. Which statement is modeled by one of the equations in the system? q is equal to d plus n 0 point 2 5 q plus 0 point 1 0 d plus 0 point 0 5 n is equal to 6 point 0 5 q plus d plus n is equal to 36

A
The total value of the coins in the jar is 36 dollars .
B
There is a total of 36 coins in the jar.
C
There is an equal number of nickels, dimes, and quarters.
D
The number of nickels is equal to the total number of dimes and quarters.
9

A picture frame has a perimeter of 40 inches. Its length is 2 inches greater than one-half its width. Let w represent the width in inches of the picture frame, and let l represent the length in inches. Which system of equations can be used to find the dimensions of the picture frame?

A
the 2 by 1 column matrix row 1 l w is equal to 40 row 2 l is equal to 2 plus 1 half w
B
the 2 by 1 column matrix row 1 2 l plus 2 w is equal to 40 row 2 l is equal to 1 half w minus 2
C
the 2 by 1 column matrix row 1 l w is equal to 40 row 2 l is equal to 1 half w minus 2
D
the 2 by 1 column matrix row 1 2 l plus 2 w is equal to 40 row 2 l is equal to 2 plus 1 half w

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