Solving pairs of linear equations in two variables

Bob's cat weighs 15 pounds and gains 2 pounds a year. His puppy weighs 9 pounds and gains 4 pounds a year. How much will they weigh when they weigh the same?

• 19

• 21

• 17

• 26

Mathematical Equivalence

ON

Answer explanation

y = x + 8 | This tree is 8 feet tall and growing 1 foot each year.

y = x/2 + 10 | This tree is 10 feet tall and growing 1/2 foot each year.

Substitute x + 8 for y in 2nd equation

x + 8 = x/2 + 10

x - x/2 + 8 -8 = x/2 - x/2 + 10 -8

x/2 = 2 | x = 4 years

Hector sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:

x + y = 21

6x + 4y = 104

• (10, 11)

• (12, 9)

• (11, 10)

• (9, 12)

The theater group sold adult and student tickets for the play.  They sold a total of 560 tickets.  Each adult ticket was $8 and each student ticket was $3.50.  The group took in a total of $3,166. How many of each type of ticket were sold for the play?  

• adult= 260
  student= 300
• adult= 210
  student= 350
• adult= 268
  student= 292
• adult= 292
  student= 268

Charlene owns a bookstore. She purchases used books from customers.

She pays $2.50 for each hardback book.

She pays $0.85 for each paperback book.

Charlene pays a customer a total of $150.10 for 121 used books.

Which system of equations could be used to determine the number of hardback books (x) & the number of paperback books (y) Charlene purchases from the customer?

• x+y=150.10

  2.50x+0.85y=121

• x+y=150.10

  0.85x+2.50y=121

• x+y=121

  2.50x+0.85y=150.10

• x+y=121

  0.85x+2.50y=150.10

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  how much the apple cost in dollar?

• 1

• 1.50

• 0.50

• 0.75

Joe bought 2 pairs of jeans and 1 shirt for $120. Sam bought 1 pair of jeans and 3 shirts for $135. How much does 1 shirt cost?

• $45.00
• $40.00
• $33.75
• $30.00

The North Decatur Band is doing a fundraiser selling butter braids attempting to earn $1,000. They are selling regular butter braids and a giant cinnamon roll braid. The regular butter braids are represented by x and cost $17 each and the giant cinnamon roll costs $30 each and is represented by y.

17x + 30y = 1000

What is the x intercept and meaning [two answers]

• (58.82, 0)

• (0, 58.82)

• If they only sold regular butter braids the band needs to sell 59 in order to meet the objective

• If they only sold giant butter braids the band needs to sell 59 in order to meet the objective

Friends and family of the bride will be helping assemble centerpieces for the wedding reception. On the right side of the room, there will be 3 round tables and 11 rectangular tables, which will require a total of 53 centerpieces. On the left side, there will be 3 round tables and 13 rectangular tables, for which they will need to assemble a total of 61 centerpieces. How many centerpieces will be on each table?

• There will be __3__ centerpieces on every round table and __4__ centerpieces on every rectangular one.

• There will be __3__ centerpieces on every round table and __4__ centerpieces on every rectangular one.

• There will be __4__ centerpieces on every round table and __5__ centerpieces on every rectangular one.

Elsa is 7 years younger than Thor. The sum of their ages is 35. How old are they?

• Elsa - 14 y/o, Thor - 21 y/o
• Elsa -21 y/o, Thor - 14 y/o
• Elsa - 7 y/o, Thor - 14 y/o
• Elsa - 14 y/o, Thor - 7 y/o