Introduction to Algebra Chapter 1.6 Translating Problems into Equations

Step 1:Read the problem CAREFULLY. Decide what the unknowns are. Decide what facts you know. Step 2:Choose a variable to represent the unknown. Write an expression for the other unknown using the original variable and one of the facts. Step 3:Reread the problem and write an equation. Use the other fact from the problem to write an equation.

Example 1: Translate into an equation The area of a rectangle is 102 cm 2. The length is 6 cm. Find the width. Solution: 1)Read. What is unknown? Facts? 2)Choose a variable: Let w = width 3)Write an equation. Area = length · width 102 = 6 · w 6w = 102

Example 2: Translate into an equation Amanda has $6 more than Bill. Together they have $30. Find how much Bill has. Solution: 1)Read. What is unknown? Facts? 2)Choose a variable: Let b = Bill’s money b + 6 = Amanda’s money 3)Write an equation. Bill + Amanda = Total b + (b+6) = 30 2b + 6 = 30

Example 3: Translate into an equation A hockey team played 12 games. They won two more than they lost. They lost one more than they tied. How many games did they win, lose and tie? Solution: 1)Read. What is unknown? Facts? 2)Choose a variable: Let l = number lost ____ = number won ____ = number tied 3)Write an equation. won + lost + tied = 12 (l + 2) + l + (l - 1) = 12 3l + 1 = 12

YOU TRY: 1.The perimeter of a rectangle is 102 cm 2. The length of the rectangle is 6 cm. (equation only). Variable: let x = ___________ other unknown = ___________ Equation: _________________ width (none) 102 = 2x + 2(6) 102 = 2x + 12

YOU TRY: 2. There are 22 students in a classroom. There are 12 more girls than boys. Find the number of boys in the classroom. (write equation only.) Variable: let x = ___________ other unknown = ___________ Equation: _________________ boys x + 12 = girls x + (x+12) = 22

YOU TRY: 3.Claire sold 25 more cards than Alice. Claire and Alice sold a total of 211 cards. Find the number of cards Alice sold. (equation only) Variable: let x = ___________ other unknown = ___________ Equation: _________________ Alice’s cards x + 25 = Claire’s cards 211 = x +(x+25)

YOU TRY: 4. The height of a tower is three times the height of a certain building. If the tower is 50 m taller than the building, how tall is the tower? Variable: let x = ___________ other unknown = ___________ Equation: _________________ building height 3x = tower height 3x = x + 50

YOU TRY: 5.The length of a rectangle is one unit more than its width. if the area is 30 square units, find the dimensions of the rectangle. Variable: let x = ___________ other unknown = ___________ Equation: _________________ width x + 1 = length 30= x (x+1)

YOU TRY: 6.A triangle has two equal sides and a third side that is 15 cm long. If the perimeter is 50 cm, how long is each of the two equal sides? Variable: let x = ___________ other unknown = ___________ Equation: _________________ length of a side (none) 50 = 2x + 15

YOU TRY: 7.Tina, Dawn and Harry have $175 together. Tina had three times as much money as Dawn. Dawn has twice as much as Harry. How much does each have? (eqn only) Variable: let x = ___________ other unknown: ___________ another unknown: ___________ Equation: _________________ Harry’s money 2x = Dawn’s money 3(2x) = Tina’s money x + 2x + 6x = 175