Understanding and solving linear equations in three variables

A basketball team has 54 points and has only made 2pt field goals and 3pt field goals. The equation 2x + 3y = 54 represents this. If the team makes nine 2pt field goals, how many 3pt field goals are made?

• 12

• 9

• 10

• 11

A used bookstore sells hardback books and paperback books.

A hardback book costs $18, including tax.

A paperback book costs $8, including tax.

Cameron bought 3 more paperback books than hardback books.

Cameron spent $154.  

How many paperback books did Cam buy?

• 5

• 6

• 7

• 8

The length of a rectangle is 6 less than three times the width. If the perimeter is 28 feet, what is the length and width of the rectangle?

• length = 18 ft. and width = 10 ft.

• length = 19.5 ft. and width = 8.5 ft.

• length = 9 ft. and width = 5 ft.

• length = 9.5 ft. and width = 4.5 ft.

Mrs. Smith is shopping in a super market and she has a budget of $86 to spend on $5 cakes, $1 eggs, $18 pizzas. She wants to buy 20 items for the coming week and must buy as many eggs as cakes and pizzas combined. How many does she need to buy?

• 6 cakes, 10 eggs, 4 pizzas

• 8 cakes, 10 eggs, 2 pizzas

• 5 cakes, 10 eggs, 5 pizzas

• 3 cakes, 10 eggs, 7 pizzas

A sandwich shop sell sandwiches for $5 each and bottles of water for $1 each. The owner of this shop needs to earn a total of $100 by the end of the day. If x is the number of sandwiches sold and y is the number of bottles of water, which equation models this problem?

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 times the team scored?

Mathematical Equivalence

ON

One pear and one apple together weigh 360 g. One pear and one banana together weigh 250g. The three fruits together weigh half of 1kg. How many grams does each fruit weigh?

• apple - 250 g

  pear - 110 g

  banana- 140 g

• apple - 110 g

  pear - 240 g

  banana- 150 g

• apple - 140 g

  pear - 250 g

  banana - 110 g

If A x B = 12,

& A + B + C = 12,

& C - A = A

Then which of the following is true?

• C = 6

• A = 3

• B = 4

• A = 2

Which statement is NOT true?

• There is 1 more heart than suns

• There are 4 more suns than moons

• There is 1 more heart than moons

• There are 3 more suns than hearts

Define two variables, write a system of equations, then solve. Sue plans to mix peppermints worth $1.20 per lb with chocolates worth $2.40 per lb to get a 40 lb mix that is worth $1.65 per lb. How much of each should she use?

• 25 lbs peppermints, 15 lbs chocolates

• 20 lbs peppermints, 20 lbs chocolates

• 15 lbs peppermints, 25 lbs chocolates

• 30 lbs peppermints, 10 lbs chocolates