Unit 2 - Equations
Day 1: Solving Simple Equations
Expression Equation
Example 1: Solve by Inspection
1) 6 + a = 11 2) 2b = 14 3)
Example 2: Solve using Opposite Operations
Adding -
Multiplying -
Squaring -
1) x + 7 = -2 2) c - 5 = -2 3) 2d = 18 4)
Example 3: Solve
1) 5a - 8 = 22 2) 75 + 5n = 225
To isolate the variable...
Example 4: Check your answer for 75 + 5n = 225
Example 5
Which is the correct solution to 2x + 5 = 21? Explain how you can tell without solving the equation.
A. x = 7 B. x = 8 C. x = 9
A high school football team has raised $1000 to spend on team jackets. The cost is $50 per jacket. Which equation can be used to solve for the number of jackets the team can buy? Explain.
A. 50 = 1000n B. 50n = 1000 C. 1000n=50n
p. 193 #8, 9, 10, 12a, 13a, 15, 17
Solving Multistep Equations
Solve
1) 2a + 3a + 1 = 11 2) 3x + 2 = 2x – 4 3) 5 - 3m = -2 +2m - 4m
Solve and check
4) 2(k + 3) - (4k - 1) = 3(k - 4) - 1
5) Is p = -2 the correct solution of this equation?
2(p + 1) = -3p - 7
6) The perimeter of this triangle is 27 m, determine the length of each side.
p. 200 #1, 6, 9 (just check f), 10a, 13
Challenge #18 - 21
Equations Involving Fractions
General Rule: Eliminate the fractions by multiplying
Examples:
1) Solve and check Instead of using distributive property, multiply both sides by 3.
2) Solve. Multiply by the lowest common denominator.
3) Solve 4) Solve
Clear the fractions.
Solve for the variable.
p. 208 #1, 4 no CAS, 6, 7, 11
Challenge #13
Modelling with Formulas
Formula – an algebraic relationship between two or more variables
Example: The area of a triangle can be determined using the formula...
If the area is 6 m2 and the height is 3 m, what is the base?
Method 1: Substitute and solve Method 2: Rearrange, then substitute
Formulas can be rearranged to isolate different variables (solving for a variable).
Examples: rearrange the formula to solve for the indicated variable
1) for
2) for
3) for r
4) for m
Modelling with Algebra
Language of Algebra
operation / + / - / x / ¸common words/phrases
Example 1
Skylar works at a ball park selling ice cream bars. He is paid $8 per hour plus a 25¢ commission for every ice cream bar he sells.
a) Write a formula to model Skylar’s total earnings.
b) If he earned $100 in 7 h of work, how many ice cream bars did he sell?
When setting up an equation, always write a “Let” statement to declare your variables.
Example 2
The sum of three consecutive integers is 81. What are the three numbers?
p. 226 #1 - 6, 9, 10 Challenge #19, 20
Warm up
1) Write the percentage as a decimal
50% 4.5% 0.2%
2) Write the decimal as a percentage
0.99 0.05
3) Write the fraction as a percentage
5 4
10 3
Applications of Percent and Proportions
1. Calculate 40% of 55.
2. 35% of a number is 7. What is the number?
3. Sales tax (HST) is 13%. How much tax is added onto a $1400 computer?
4. You pay $789.87 for a new computer. What was the price before tax?
5. A $45 sweater is on sale for 15% off. What is the sale price of the sweater?
6. Susan earns 5% commission on her sales. If she made $400 last week, how much did she sell?
7. In a hydrochloric acid solution, 5% is pure hydrochloric acid and 95% is water. If you have a 60mL bottle of the solution, how much of it is pure acid?
Worksheet and Textbook p. 237 #4 - 8
Warm up
You are buying a pair of $75 jeans. They are on a 10% off sale rack.
1) What is the sale price of the jeans?
2) How much will you have to pay for the jeans with HST?
Applications of Percent and Proportions - Day 2
1) Joe earns $5 per hour and 4% commission on his sales.
a) Create an equation to model Joe's total earnings.
b) If he earned $450 in 6 hours of work, what were his total sales?
2) Share the Profits (from last year's EQAO)
Three partners, Luc, Deborah and Melanie, share the profits of a business in the ratio 2:3:7 respectively.
The profit for this year is $176 496.
Determine the share of the profit for each partner.
3) Swedish Berries cost $0.25/kg at the Bulk Barn. How much does it cost if you buy 5 pounds?
1 kilogram = 2.2 pounds
4) One mile is equivalent to 1.6 km.
a) How many miles are there in 5 km?
b) How many kilometers are there in 27 miles?