algebra part 1

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 1 options:

Question 2 (5 points)

Use substitution to solve the system of equations.

y = 2
x + 16

2x – 7y = –64

Question 2 options:

	(–4, 8)
	(–1, 11)
	(8, –4)
	(–7, –11)

Question 3 (5 points)

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

Question 3 options:

	elimination using subtraction;
	elimination using addition;
	elimination using subtraction;
	elimination using addition;

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 4 options:

Question 5 (5 points)

Use elimination to solve the system of equations.

–9
x – 2
y = –115

–6x + 2y = –110

Question 5 options:

	(10, 4)
	(15, –10)
	(–15, 10)
	(–10, –4)

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 6 options:

	20 cm and 55 cm
	20 cm and 45 cm
	10 cm and 45 cm
	10 cm and 40 cm

Question 7 (5 points)

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

Question 7 options:

	no solution
	infinitely many
	two
	one

Question 8 (5 points)

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

Question 8 options:

	10, 42
	9, 43
	9, 61
	9, 45

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 9 options:

	10 h
	7.5 h
	5.5 h
	2 h

Question 10 (5 points)

Solve the system of inequalities by graphing.

Question 10 options:

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 11 options:

	one solution; (1, 0)
	one solution; (0, 1)
	no solution
	infinitely many

Question 12 (5 points)

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

Question 12 options:

	elimination using addition;
	elimination using multiplication;
	elimination using multiplication;
	elimination using subtraction;

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 13 options:

Question 14 (5 points)

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

Question 14 options:

	74° and 106°
	32° and 58°
	29° and 61°
	21° and 69°

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 15 options:

	15
	12
	31
	17

Question 16 (5 points)

Use substitution to solve the system of equations.

18 =
x – 3
y

2x + 19 = –5y

Question 16 options:

	(3, –5)
	(6, 10)
	(–11, 9)
	infinitely many solutions

Question 17 (5 points)

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

Question 17 options:

	39 and 51
	35 and 47
	31 and 59
	no solution

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 18 options:

	300 adults, 400 children
	400 adults, 1100 children
	400 adults, 300 children
	600 adults, 100 children

Question 19 (5 points)

Solve the system of inequalities by graphing.

Question 19 options:

Question 20 (5 points)

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

Question 20 options:

	one
	infinitely many
	no solution
	two

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