Writing Equations

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. If we want to know how many horses and chickens are in the barn, how would you define the variables. Use h and c for the variables and use words after = sign.

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?

• h + c = 15

  4h + 2c = 44

• 4h + 2c = 15

  h + c = 44

• h = 2c + 44

  4h = c + 15

• 2h - 4c = 44

  h - c = 15

Suppose you have a total of $2.25 in dimes and nickels. You have twice as many dimes, as nickels. Which system of equations could be used to determine how many of each you have?

• 0.10d + 0.05n = 2.25

  d = 2n

• 0.05d + 0.10n = 2.25

  d = 2n

• 0.10d + 0.05n = 2.25

  n = 2d

• 0.05d + 0.10n = 2.25

  n = 2d

Edwin bought 3 cd's and 7 dvd's for $80.  Jessica bought 6 cd's and 3 dvd's for $63.75.  Which system of equations could be used to determine how much one cd and one dvd costs?

• 3x + 7y = 80
  6x + 3y = 63.75
• 3x + 3y = 80
  6x + 7y = 63.75
• 3x + 7y = 63.75
  6x + 3y = 80
• 6x + 7y = 80
  3x + 3y = 63.75

Academy sports equipment store is having a sale on bike helmets and water bottles.  One bike club purchased 10 helmets and 2 water bottles for $155.  Another bike club purchased 12 helmets and 3 water bottles for $189.  Which system of equations could be used to determine the cost of a bike helmet and a water bottle?

• 2h + 10b = 155
  12h + 3b = 189
• 10h + 2b = 189
  12h + 3b = 155
• 10h + 2b = 155
  12h + 3b = 189
• 10h + 3b = 155
  12h + 2b = 189

Charlie had $115 and is earning $50 per week at a summer job. Eduardo had $130 and is earning $40 per week at a summer job. Which system of equations could be used to determine how many weeks (w) they must work to have the same amount (A)?

• A = 115 + 40w

  A = 130 + 50w

• A = 115 - 50w

  A = 130 - 40w

• A = 50 + 115w

  A = 40 + 130w

• A = 115 + 50w

  A = 130 + 40w

Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken dinner for $14 and the rest order steak dinner for $17. The total bill is $99. If we want to know how many of our family ordered chicken dinners and how many ordered steak dinners,

how would you define the variables for this problem?

Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken dinner for $14 and the rest order steak dinner for $17. The total bill is $99. Write a system that could represent this situation.

• c + s = 6

  14c + 17s = 99

• c + s = 99

  14c + 17s = 6

• c + s = 6

  17c + 14s = 99

• c + s = 99

  17c + 14s = 6

Ashley had a summer lemonade stand where she sold small cups of lemonade for $1.25 and large cups for $2.50. If Ashley sold a total of 155 cups for $265, which system could be used to determine the number of small (x) and large (y) cups she sold?

• x + y = 265

  1.25x+2.5y=155

• x + y = 155

  2.5x+1.25y=265

• x + y = 265

  2.5x+1.25y=155

• x + y = 155

  1.25x+2.5y=265

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Which equations represents the system that could be used? 

• 1s + 3c = 38
  2s + 3c = 52
• 3s + 1c = 38
  3s + 2c = 52
• s + c = 38
  s + c = 52
• 3s + 3c = 38
  1s + 2c = 52