Substitution Story Problems

Substitution Story Problems

Steps to solving a system of equation story problem:

• Write down the equations.

• Plug equation 1 into equation 2.

• Solve for x.

• Plug x back into equation 1.

• Solve for y.

• Write your solution in the form (x, y) or with appropriate labels.

Razorback Basketball

April 4th, 1994 was the most important game in Arkansas Razorback Basketball history. The national title game against Duke University.

Multiple Choice

Corliss Williamson, the Razorbacks best player had a total of 31 points and rebounds combined. His total points was the same as one less than three times is total rebounds.

Which set of equations represent the system?

• p - r = 31

  p = 3r + 1

• p + r = 31

  p = r - 3

• p - r = 31

  r = 3p - 1

• p + r = 31

  p = 3r - 1

Multiple Choice

Corliss Williamson, the Razorbacks best player had a total of 31 points and rebounds combined. His total points was the same as one less than three times is total rebounds.

How many rebounds and points did Corliss have?

• 20 points

  11 rebounds

• 23 points

  8 rebounds

• 22 points

  10 rebounds

• 19 points

  12 rebounds

Chick-Fil-A Menu

One of Mr. Lewis' favorite gifts from students is gift cards to his favorite resteraunts. Let's look at a few ways to spend a $25 gift card.

Multiple Choice

For exactly $25, Mr. Lewis could buy 4 chicken sandwiches and 2 medium drinks. It is also worth noting that the price of a chicken sandwich is double the price of a medium drink.

Which set of equations represent the system?

• 4s + 2d = 25

  s = 2d

• 4s + 2d = 25

  d = 2s

• 2s + 4d = 25

  s = 2d

• 2s + 4d = 25

  d = 2s

Multiple Select

It would cost $21 to buy 2 nuggets, 2 fries, and 2 medium drinks. An order of nuggets cost $1 more than an order of fries.

Which set of equations represent the system? (choose at least 2.)

(Remember medium drinks cost $2.50.)

• 2n + 2f + 2(2.5) = 21

  n = f + 1

• 2n + 2f + 5 = 21

  n = f + 1

• 2n + 2f = 16

  n = f + 1

• 2n + 2f = 26

  n = f + 1

Multiple Choice

It would cost $21 to buy 2 nuggets, 2 fries, and 2 medium drinks. An order of nuggets cost $1 more than an order of fries.

Which shows the correct first step to solving the system?

2n + 2f = 16

n = f + 1

• 2n + 2(n + 1) = 16

• 2(f + 1) + 2f = 16

• (n + 1) + 2f = 16

• 2f + 1 + 2f = 16

Multiple Choice

Which shows the correct next steps to solving the system?

2n + 2f = 16

n = f + 1

2(f + 1) + 2f = 16

• 2f + 2 + 2f = 16

  4f + 2 = 16

  4f = 14

  f = 3.5

• 2f + 1 + 2f = 16

  4f + 1 = 16

  4f = 15

  f = 3.75

• 2f + 2 + 2f = 16

  4f + 2 = 16

  4f = 18

  f = 4.5

• 2f + 1 + 2f = 16

  4f + 1 = 16

  4f = 17

  f = 4.25

Multiple Choice

It would cost $21 to buy 2 nuggets, 2 fries, and 2 medium drinks. An order of nuggets cost $1 more than an order of fries.

Now that you know that fries cost $3.50.

How much does an order of nuggets cost?

• $3.50

• $5.00

• $2.50

• $4.50

Hot Dog Eating

Nathan's Hot Dog Eating contest is an annual event where competitive eaters scarf down as many hot dog's as possible in a 10 minute time frame.

Multiple Choice

In 2017, Joey Chestnut set the world record by consuming 72 hotdogs. In total, Joe consumed an astronomical 19,440 calories. (That's almost 10 days worth the recommended daily intake.)

The amount of calories in a hot dog bun is 900 less than 8 times the total calories in a hotdog.

Which set of equations represents the system?

• 72h + 72b = 19440

  h = 8b - 900

• 72h + 72b = 19440

  b = 8h + 900

• 72h + 72b = 19440

  b = 8h - 900

• 72h + 72b = 19440

  b = 900 - 8h

Multiple Choice

In 2017, Joey Chestnut set the world record by consuming 72 hotdogs. In total, Joe consumed an astronomical 19,440 calories. The amount of calories in a hotdog bun is 900 less than 8 times the total calories in a hotdog.

72h + 72b = 19440

b = 8h - 900

Solve the system.

• Buns are 200 calories.

  Hotdogs are 150 calories.

• Buns are 120 calories.

  Hotdogs are 60 calories.

• Buns are 130 calories.

  Hotdogs are 140 calories.

• Hotdogs are 130 calories.

  Buns are 140 calories.

Dueling Pizza Companies

Toni's and Mama Y's Pizza both claim to have the best pizza prices in town.

Multiple Select

At Toni's, a large pizza cost $5.50 for a medium hand tossed pizza. Each topping cost an additional 50 cents.

At Mama Y's Pizza, every two pizza toppings cost a dollar, and a medium pizza is $6.00 to start. However, if you say, "Mama sent me" when you check out, you always get 50 cents of your order.

Assuming you always get the discount, who has cheaper pizza?

• Mama Y's

• Toni's

Multiple Choice

How many solutions does the pizza problem have?

• One Solution

• No Solutions

• Infinite Solutions

Dueling Pizza (Infinite Solution.)

• That may have been a trick question... sorry.

• Those pizza's cost the same, therefore, they will have infinite solutions. I'll show you the equations.

• Toni's Pizza - C = 5.50 + 0.5t

• Mama Y's - C = 6.00 - 0.5 + 0.5t (Which simplifies to look just like Toni's equation.)

Multiple Choice

Dan and Craig are running a race. Both Dan and Craig run about 10 meters per second. However, Dan gets a 1 second head start. Who wins the race?

• Dan

• Craig

Multiple Choice

Dan and Craig are running a race. Both Dan and Craig run about 10 meters per second. However, Dan gets a 1 second head start.

What do their equations look like?

• d = 10s + 1

  d = 10s

• d = 10s

  d = 10s

• d = 10s - 1

  d = 10s

• d = 10s + 1

  d = 10s - 1

Multiple Choice

How many solutions does the system with Dan and Craig have?

• One Solution

• Infinite Solutions

• No Solution

Dan and Craig

Dan wins the race in the previous questions clearly. The reason being they run the same speed, but he just gets a head start. Their speed represents their slope, and when two equations have the same slope, but different starting points, then the lines will never touch, and have no solution.

Poll

How do you feel about solving systems with substitution?

• This is always easy.

• This is sometimes easy.

• This is sometimes challenging.

• This is always challenging.