Question

A. Renard let’s t= the number of taffy bags and c= the number of Carmel bags. Help him write two equations to represent the information in the problem.

b. Now are are is stuck. He says, “if both of the equations were in the form ‘t= something’, I could set the two expressions equal to each other to find the solution.” Help him rewrite the equations into a form he can use to solve the problem.


c. Solve Renard’s system of equations to find the number of bags of Carmel and number of bags of taffy that Ariel bought.


d. How you can verify that your solution is correct?

Answer 1

• 20 taffy bags and 15 caramel candy bags

Explanation:

Given:

• t = the number of taffy bags
• c = the number of caramel bags
• Number of taffy's are 5 more than caramel bags
• Taffy bags weigh 8 ounces and caramel bags weigh 16 ounces
• Total weight is 400 ounces

Equations:

• t = c + 5 (the difference in number of bags)
• 8t + 16c = 400 (the weight of the bags)

Simplify the second equation by dividing all terms by 8:

• t + 2c = 50

Substitute t and solve for c:

• c + 5 + 2c = 50
• 3c = 50 - 5
• 3c = 45
• c = 45/3
• c = 15

Find the value of t:

• t = 15 + 5 = 20

Answer:

• 20 taffy bags and 15 caramel candy bags