Understanding and solving linear equations in three variables

Coach Anthony has a jar full of change. There are 37 nickels, dimes, and quarters. The total of the coins is $3.75. If there are twice as many nickels than dimes, how many of each does he have?

• 20 dimes, 10 nickels, 7 quarters

• 10 dimes, 20 nickels, 7 quarters

• 9 dimes, 18 nickels, 10 quarters

Carlos called within Canada, to the United States, and to Mexico during the month of December. The charges are 28¢/min within Canada, 30¢/min to the U.S., and 84¢/min to Mexico. Calculate the number of minutes that if his total bill for the month was $90.96, he talked twice as long to Mexico as he did to the U.S., and the total number of minutes spent talking within Canada and to Mexico was 122.

• 32 minutes within Canada

  30 minutes to the U.S.

  60 minutes to Mexico

• 47 minutes within Canada

  25 minutes to the U.S.

  50 minutes to Mexico

• 42 minutes within Canada

  40 minutes to the U.S.

  80 minutes to Mexico

• 77 minutes within Canada

  15 minutes to the U.S.

  30 minutes to Mexico

Joey has a collection of action figures. He separates them into small, medium, and large figures. He has 4 times as many small figures as medium figures. The number of large figures is 6 less than 2 times the number of medium figures.

He has a total of 43 action figures. He has 7 medium figures. How many small and large figures does he have?

• small = 28

• small = 7

• large = 8

• large = 20

A football team scored a total of 80 points in one game.  They scored 24 times.  The scoring was made up of touchdowns (6 points), PATs (1 point), and field goals (3 points).  They had three more touchdowns than field goals.  If x represents touchdowns, y represents points after touchdowns (PATs), and z represents field goals, write an equation that represents the total points scored?

Mathematical Equivalence

ON

Amy wants to buy soda AND pizza for her Halloween party. She has $45 to spend. One case of soda costs $4, and one pizza costs $8. Write an equation that could be used to find a valid combination for as many cases of soda, x, and pizzas, y, as she can afford.

• 8x + 4y = 45

• 4x - 8y = 45

• 12xy = 45

• 4x + 8y = 45

Sofia is making a batch of slime using a recipe that includes glue, water, and a salt solution. She uses 7.5 fl oz of glue. The amount of glue is 12.5 times the amount of salt solution. There are 4.2 less fluid ounces of salt solution than water.

How many fluid ounces of water does Sofia use to make a batch of slime? (rounded to the nearest tenth)

• 2.5

• 3.6

• 4.8

• 5.9

Solve.

• 81

• 101

• 110

• 84

Devon owns a house-cleaning company that has to give price quotes to potential clients. He figures out his price by assuming a $25.00 base charge and then adding 18.00 for each bathroom and $14.00 for every other room. If he uses P for price, B for Bath, and R for other Rooms, which formula represents the price quote formula?

• $P=18B+14R$

• $P=18B+14R\ -25$

• $P=18B+14R+25$

• $P=32BR\ +25$

17)

• L=3W

  2L+2W=86

• W=3L

  L+W=86

• W=3L

  2L+2W=86

Divide 150 into three parts such that the second number is five - sixth the first and the third number is four - fifths the second.

• 20, 90, 40

• 60, 50,40

• 30, 50, 40

• 90, 80, 70