Lesson 13: Using Algebra to Solve Problems
Learning Goal…By the end today's lesson I will be able to...--interpret the intention of a given word problem. Define variables and use them to set up an equation.Use the strategies of the unit to solve the equation.
Success Criteria…I have achieved today's goal when I can correctly solve today's consolidate question.
Example 0: Thinking Page from the last Quiz
Example 1: Translate the following phrases into an algebraic representation.
a) six more than a number
b) three less than four times a number
c) six more than half a number is 20
d) three times, two less than a number
e) the product of a number and three less than the number is 15
Solving Word Problems:
1)Define your variable(s). Create ______for each.
2) Create______with the given information.
3)______the term that ______the variable.
4)Isolate the ______.
5) Write a ______statement.
Example 2: The sum of three consecutive even integers is 384. What are the three numbers? (With steps)
a) Give an expression for each integer.
b) Give an equation for the sum of the integers.
c) Determine the value of each integer.
Answer the following on the back.
Example 3: Two brothers are 5 years apart. The sum of their ages is 21. How old is the older brother? (No Steps)
Example 4: Together, Al, Betty and Cathy, ate 118 Smarties. Betty had twice as much as Cathy and Cathy had 10 more than Al. How many Smarties did each friend eat?
Translating Verbal Statements into Equations
Express each of the following problems algebraically.
(Hint: Use n as the unknown number and create an equation from the problem.)
/ 7 more than 2 times a number
/ The product of 5 and a number is 10
six times a number, less 11
/ two less than three times a number is 28
/ Twice the sum of a certain number and 26
100 less than a number equals -70
/ 12 less than twice a number
/ six times the sum of a number and 4 is 42
99 less than a number
/ The sum of a number and eleven times the same number
/ A number increased by 2 is 26
5 less than the product of 9 and a number is 22
/ The sum of 43 and a number
/ One-tenth of a number is 20
eight times a number equals 8 more than the number
/ twelve times a number added to 10
/ The sum of 10 and the product of 4 and a number is 22
One-sixth of a number is 66
/ The sum of 10 and the product of 5 and a number is 55
/ six times the sum of a number and 2 is 24
A number minus 9 is -7
/ The sum of a number and five times the same number is 12
/ 13 less than twice a number is -5
A number increased by 83 is 105
/ five times a number, less 12 is 48
/ six less than two times a number is 16
one times a number added to 4
/ nine times a number equals 63
/ 10 less than the product of 6 and a number is 32