Non-linear equations (multi-variable)

Type one of the missing answers.

A sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. Each issues of the sports magazine has 18 fewer pages than each issue of the technology magazine.

Which system of equations can be used to find s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine?

• s = t - 18

  12s = 10t + 32

• t = s - 18

  10t = 12s + 32

• s = t - 18

  10s = 12t + 32

• t = s - 18

  12t = 10s + 32

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

• 3H + 2D = 315

  2H + 4D = 450

• 3H + 2D = 450

  2H + 4D = 315

• 2H + 4D = 315

  3H + 2D = 450

• 3H + 2D = 315

  2H + 2D = 135

Sam ordered 4 tacos and 5 enchiladas for lunch at the restaurant. His bill came to $10.80. Which equation matches the given situation?

• 4x + 3y = 8.10

• 4x + 5y = 10.80

• 4x - 5y = 10.80

• 4x + 10.80y = 5

A sporting goods store sells left handed (L) and right handed (R) gloves. In one month, a total of 12 gloves were sold for a total of $561. Right handed gloves cost $45 each and left handed gloves cost $52. Which system could be solved to determine the number of each type of glove sold?

• L + R = 561

  45L+52R =12

• L + R = 12

  45R + 52L =561

• L + R = 12

  45L+52R =561

• L + R = 561

  45R + 52L =12

An electronics store advertised a 19-inch model TV for $349 and a 25-inch model TV for $469.  During one month they sold 44 TVs total and profited an amount of $17,516.  If x represents the number of 19-inch TVs and y represents the number of 25-inch TVs, which system of equation best describes this situation?

 

A)   x + y = 44                        B)    x + y = 44                      

  349x + 469y = 17,516               19x + 25y = 17,516                  

 

C)  349x + 469y = 44            D)   19x + 25y = 44

       x + y = 17,516                       349x + 469y = 17,516

 

E)  None of the above.

• A

• B

• C

• D

• E

Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are $20 bills and $50 bills. How many of each bill does Caitlin have?  Which system best represents the situation? 

• x + y = 1430
  20x + 50y = 49
• x + y = 49
  10x + 5y = 1430 
• x + y = 49
  20x + 50y = 1430
• x + y = 49
  x + y = 1430

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 and nickels?

• 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

The admission fee at a small fair is $2 for children and $4 for adults. On a certain day $5,050 is collected. Write an equation to model this situation. No spaces. Use x and y.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If e=Erin's age and a=Alex's age, choose the system that matches the situation.

• e + a = 33
  a = 2e - 3
• a + e = 33
  e = 2a - 3
• a + e = 33
  a = 3 - 2e
• e + a = 33
  e = 33 - 2e