# algebra part 1 5

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## Question 1 (5 points)

Dylan has 15 marbles. Some are red and some are white. The number of red marbles is three more than six times the number of the white marbles. Write a system of equations that can be used to find the number of white marbles, *x*, and the number of red marbles, *y*.

## Question 2 (5 points)

*Use substitution to solve the system of equations.*

*y* = 2

*x* + 16

2*x* â€“ 7*y* = â€“64

## Question 3 (5 points)

*Determine the best method to solve the system of equations. Then solve the system.*

## Question 4 (5 points)

A hotel has 150 rooms. The charges for a double room and a single room are $270 per night and $150 per night respectively. On a night when the hotel was completely occupied, revenues were $33,300. Which pair of equations can be used to determine the number of double room, *d*, and the number of single room, *s*, in the hotel?

## Question 5 (5 points)

*Use elimination to solve the system of equations.*

â€“9

*x* â€“ 2

*y* = â€“115

â€“6*x* + 2*y* = â€“110

## Question 6 (5 points)

One line segment is 5 cm more than 4 times the length of another. The difference in their lengths is 35 cm. How long are they?

## Question 7 (5 points)

*Use the graph below to determine the number of solutions the system has.*

## Question 8 (5 points)

The sum of Jack and his fatherâ€™s ages is 52. Jackâ€™s fatherâ€™s age is 2 less than 5 times Jackâ€™s age. Find the ages of Jack and his father.

## Question 9 (5 points)

Amber and Austin were driving the same route from college to their home town. Amber left 2 hours before Austin. Amber drove at an average speed of 55 mph, and Austin averaged 75 mph per hour. After how many hours did Austin catch up with Amber?

## Question 10 (5 points)

*Solve the system of inequalities by graphing.*

## Question 11 (5 points)

*Graph the system of equations. Then determine whether the system has* no *solution,* one *solution, or* infinitely many *solutions. If the system has one solution, name it.*

## Question 12 (5 points)

*Determine the best method to solve the system of equations. Then solve the system.*

## Question 13 (5 points)

The cost of 3 large candles and 5 small candles is $6.40. The cost of 4 large candles and 6 small candles is $7.50. Which pair of equations can be used to determine, *t*, the cost of a large candle, and *s*, the cost of a small candle?

## Question 14 (5 points)

Angle *A* and angle *B* are complementary, that is their measurements add up to 90Â°. Angle *B* measures 32Â° more than angle *A*. What are the measurements of the two angles?

## Question 15 (5 points)

Jordan is 3 years less than twice the age of his cousin. If their ages total 48, how old is Jordan?

## Question 16 (5 points)

*Use substitution to solve the system of equations.*

18 =

*x* â€“ 3

*y*

2*x* + 19 = â€“5*y*

## Question 17 (5 points)

The sum of two numbers is 90. Their difference is 12. What are the numbers?

## Question 18 (5 points)

The admission fee of a theater is $2.50 for adults and $1.25 for children. On a certain day, 700 people went to the theater for a concert and $1,375 was collected. How many children and how many adults attended the concert?

## Question 19 (5 points)

*Solve the system of inequalities by graphing.*

## Question 20 (5 points)

*Use the graph below to determine the number of solutions the system has.*

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