Understanding and generating non-linear equations in two or more variables

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• s + a = 530

  3s + 4a = 1740

• s + a = 530

  4s + 3a = 1740

• s + a = 1740

  3s + 4a = 530

• s + a = 1740

  4s + 3a = 530

You have a total of 17 coins.  All of your coins are nickels and dimes.  The total value of the coins is $1.35.  Which system of equations represents this situation?

• n+d=17
  .05n+.10d=1.35
• .05n+.10d=17
  n+d=1.35
• .25n+.10d=1.35
  n+d=17

Kacey is thinking of two numbers. Their sum is -18. Their difference is 38.

Let x = smaller number, y = larger number.

Write a system of equations that could be used to find the two numbers.

A bag contains green marbles and blue marbles, 26 in total. The number of green marbles is 1 more than 4 times the number of blue marbles.

Write a system of equtions that could be used to determine the number of each color of marble. Choose two equations.

• g + b = 26

• g = 4b + 1

• g + b = 4b + 1

• 4b + 1 = 26

Dennis mowed his next door neighbor’s lawn for a handful of dimes and nickels, 80 coins in all. Upon completing the job he counted out the coins and it came to $6.60. Which system of equations could be used to find the exact number of dimes (d) and nickels (n)?

• d + n = 6.60

  .10d + .05n = 80

• d + n = 80

  d + n = 6.60

• d + n = 80

  .10d + .05n = 6.60

• d + n = 80

  .05d + .10n = 6.60

Mr. Newman bought 8 tickets to a chili supper and spent a total of $30.  He bought a combination of adult tickets for $5 each and child tickets $3 each.  Which system of equations below will determine the number of child tickets, c, and the number of adult tickets, a, he bought?

 

A)  8a + 5c = 30             B)   a + c = 8

        a + c = 3                      3a + 5c = 30

 

C)   5a + 3c = 8              D)  5a + 3c = 30

         a + c = 30                     a + c = 8

 

E) None of the above

• A

• B

• C

• D

• E

3b) Write a system of equation for the following word problem:

The school that James does to is selling tickets to the annual dance competition. On the first day of tick sales the school sold 2 adult tickets(x) and 9 child tickets (y) for a total of $109. The school took in $186 on the second day by selling 12 adult tickets and 2 child tickets. What is the price of one adult ticket and one child ticket?

WRITE THE SECOND EQUATION

Mathematical Equivalence

OFF

Beyonce wanted to host a barbecue for Spring Break next week. A package of hot dogs cost $1.60, and a package of hamburgers costs $5. Beyonce bought a total of 8 packages of meat and spent $23 total. Write a system for this situation. Assume "x" represents # of hot dog packages and "y" represent # of hamburger packages.

• x + y = 8
  1.60x + 5y = 23
• x + y = 23
  1.60x + 5y = 8
• x + y = 8
  1.60y + 5x = 23
• x + y = 23
  1.60y + 5x = 8

How many people like both skateboards & snowmobiles?

• 45

• 25

• 10

• 80

What equation could we write for Clara's plant purchase?