Alg 1, Lesson 4.1.2: One Equation or Two?

Alg 1, Lesson 4.1.2: One Equation or Two?

4-21

Ariel bought several bags of caramel candy and taffy. The number of bags of taffy was 5 more than the number of bags of caramels. Taffy bags weigh 8 ounces each, and caramel bags weigh 16 ounces each. The total weight of all of the bags of candy was 400 ounces. How many bags of candy did she buy?

Multiple Choice

Ariel bought several bags of caramel candy and taffy. The number of bags of taffy was 5 more than the number of bags of caramels. Taffy bags weigh 8 ounces each, and caramel bags weigh 16 ounces each. The total weight of all of the bags of candy was 400 ounces. How many bags of candy did she buy?

a) Renard lets t= the number of taffy bags and c= the number of caramel bags.  Help him write two equations to represent the information in the problem.

•  $t=5+c$  
   $8t+16c=400$  
  

•  $t=5c$  
   $8t+16c=400$  
  

•  $c=t+5$   $16t+8c=400$  

•  $t=c$ 
  
    $t+c=400$  

Multiple Choice

b) Now Renard is stuck. He says, “If both of the equations were in the form ‘t= something,’ I could set the two equations equal to each other to find the solution.” Help him change the second equation into "t=" form. 
 $t=5+c$  

 $8t+16c=400$ 

•  $t=400-16c$  

•  $c=25-\frac{1}{2}t$  

•  $t=50-2c$  

•  $c=400-8t$  

Multiple Choice

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

• 
  

  $t=20,\ c=15$
  

• $c=15,\ t=20$

• $t=10,\ c=30$

• $c=50,\ t=100$

Multiple Choice

d) How you can make sure your solution is correct?

• Ask your buddy

• Use a lifeline from Who Wants to be a Millionaire

• Plug your answers for t and c back into the original equations

Multiple Choice

4-22

Notice that the second equation is solved for y, but the first is not. Change the first equation into “y=” form.

 $x-2y=4$  

 $y=-\frac{1}{2}x+4$  

•  $y=-\frac{1}{2}x+4$  

•  $x=2y+4$  

•  $y=-x+6$  

•  $y=\frac{1}{2}x-2$  

Multiple Choice

Solve the system of equations.

 $y=\frac{1}{2}x-2$  

 $y=-\frac{1}{2}x+4$  

•  $\left(-1,\ 2\right)$  

•  $\left(6,\ 1\right)$  

•  $\left(2,\ -1\right)$  

•  $\left(1,\ 6\right)$  

Open Ended

Check you solution by plugging it back in to the equations. Then write down if you know how to check it.

4-23

A set of two or more equations with the same variables is called a system of equations. When you set the two equations equal to each other, like Renard did in problem 4-21, you are using the equal values method of solving a system of equations.

Multiple Choice

4-23

There are 21 animals on Farmer Cole’s farm – all sheep and chickens. If the animals have a total of 56 legs, how many of each type of animal lives on his farm? Write a system of equations, and use the equal values method to solve it. Be sure to check your answer.

• 100,000 sheep, 1 million chickens

• 7 sheep, 14 chickens

• 14 sheep, 7 chickens

• 1 sheep, 1 chicken

4-24

Solve the system of equations below using the Equal Values Method. Check your answer.

 $x+2y=14$  

 $-x+3y=26$  

Multiple Choice

What's your answer to problem 4-24?

 $x+2y=14$  
 $-x+3y=26$  

• $\left(8,\ -2\right)$

• $\left(5,\ -3\right)$

• $\left(10,\ 1\right)$

• 
  

  $\left(-2,\ 8\right)$