Formulate Equations

Lesson 6 (3rd 6 Weeks)TEKS 6.5

Equation

• Describes a relationship between two quantities

• A mathematical sentence stating that two quantities or expressions are equal

Variable

• A letter representing an unknown quantity

• Any letter can be chosen for a variable

To formulate an equation that represents a problem

• Write an expression to represent each quantity

• Use a variable to represent an unknown quantity

• Look for a relationship between the quantities in the problem

• Write an equation that represents the relationship

ExampleMatthew had $50 for his trip to Fiesta, Texas. He bought 2 ride tickets that cost $5.50 each. Then he spent $9 for food. Which equation can be used to find x, the amount of money Matthew has left?

A. x = 50.00 – 5.50 - 9B. x = 50.00 + 5.50 – 9C. x = 50.00 – (2 • 5.50) – 9D. x = 50.00 – (2 • 5.50) + 9

Matthew had $50 for his trip to Fiesta, Texas. He bought 2 ride tickets that cost $5.50 each. Then he spent $9 for food. Which equation can be used to find x, the amount of money Matthew has left?

A. x = 50.00 – 5.50 - 9B. x = 50.00 + 5.50 – 9C. x = 50.00 – (2 • 5.50) – 9D. x = 50.00 – (2 • 5.50) + 9

Look at A & B, notice that the equation only has Matthew buying 1 ride ticket. In the problem he bought 2, so we know both of these answers are wrong.

Matthew had $50 for his trip to Fiesta, Texas. He bought 2 ride tickets that cost $5.50 each. Then he spent $9 for food. Which equation can be used to find x, the amount of money Matthew has left?

A. x = 50.00 – 5.50 - 9B. x = 50.00 + 5.50 – 9C. x = 50.00 – (2 • 5.50) – 9D. x = 50.00 – (2 • 5.50) + 9

Answers C & D both have him buying 2 ride tickets but C has him subtracting 9 from the $50 while D has him adding 9 to the $50. Since when we purchase items it takes money out of our pockets (subtracting), C is my answer

ExampleBalloons at the party store cost $1.50 each, plus a one-time cost of $3 to have the balloons filled with helium. Which equation can be used to find c, the cost of filled balloons for b balloons?

A. c = 3b + 1.50B. c = 1.50(b + 3)C. c = 1.50b + 3D. c = 3(b + 1.50)

Balloons at the party store cost $1.50 each, plus a one-time cost of $3 to have the balloons filled with helium. Which equation can be used to find c, the cost of filled balloons for b balloons?

A. c = 3b + 1.50B. c = 1.50(b + 3)C. c = 1.50b + 3D. c = 3(b + 1.50)

Let’s start by looking at A. A has us multiplying 3 by the number of balloons (b). In the problem it says the $3 is for a one time cost, which means we wouldn’t multiply it.

Balloons at the party store cost $1.50 each, plus a one-time cost of $3 to have the balloons filled with helium. Which equation can be used to find c, the cost of filled balloons for b balloons?

A. c = 3b + 1.50B. c = 1.50(b + 3)C. c = 1.50b + 3D. c = 3(b + 1.50)

B has us adding the one time cost with the number of balloons and then multiplying it by the cost of each balloon. We don’t need to multiply the one time cost.

Balloons at the party store cost $1.50 each, plus a one-time cost of $3 to have the balloons filled with helium. Which equation can be used to find c, the cost of filled balloons for b balloons?

A. c = 3b + 1.50B. c = 1.50(b + 3)C. c = 1.50b + 3D. c = 3(b + 1.50)

C has us multiplying the number of balloons by the cost of each balloon and then adding in the $3. This makes the most sense.

Balloons at the party store cost $1.50 each, plus a one-time cost of $3 to have the balloons filled with helium. Which equation can be used to find c, the cost of filled balloons for b balloons?

A. c = 3b + 1.50B. c = 1.50(b + 3)C. c = 1.50b + 3D. c = 3(b + 1.50)

D has us adding the cost of each balloon by the number of balloons and then multiplying by the one time cost.

So the only answer that makes sense is C.