- Solving equations from word problemsMacDonald

Math 9

Expressions can be translated directly to an English sentence

14 + n fourteen increased by a number

11 n eleven reduced by a number

Words are nothing more than a longer version of what you are already looking at!

Synonyms are different words with almost identical or similar meanings

Lets review some of the words we use in association with our normal math operators:

+ - x

Synonyms are different words with almost identical or similar meanings

Lets review some of the words we use in association with our normal math operators:

+ - x- plus - minus- times - divided by- sum - difference- product - quotient- increased by - decreased by- double - halve - reduced by

How do we do it?

Why are they so hard?

I just dont get it!

Forget it . Im done.

What is the most difficult part about these:

The first side of a triangle is seven cm shorter than twice the second side. The third side is four cm longer than the first side. The perimeter is eighty cm. Find the length of each side.

Matt is 3 times as old as Jenny. In 15 years, their ages will total 58. How old is each person now?

Find three even numbers in a row whose sum is 156.

What is the most difficult part about these:

The first side of a triangle is seven cm shorter than twice the second side. The third side is four cm longer than the first side. The perimeter is eighty cm. Find the length of each side.

Matt is 3 times as old as Jenny. In 15 years, their ages will total 58. How old is each person now?

Find three even numbers in a row whose sum is 156.

1. Draw any necessary diagrams to provide a visual. Read sentences one at a time to slow down your racing thoughts.

2. Define any variables. This is sometimes referred to as a Let statement. You assign a variable to anything you do not know. (What are you looking for?)

3. Create an equation using the variable(s)

4. Solve for any unknown values

The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.

The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.Let b represent Side BA = 2B

B = B

C = 2B + 1

The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.A = 2B

B = B

C = 2B + 1

The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.a + b + c =76

(2B)+B+(2B+1)=76

The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.a + b + c =76

(2B)+B+(2B+1)=76

5B+1=76

5B=75

b= 15 cm

The perimeter of a triangle is seventy-six cm. Side a of the triangle is twice as long as side b. Side c is one cm longer than side a. Find the length of each side.a + b + c =76

(2B)+B+(2B+1)=76

5B+1=76

5B=75

b=15 cma= 2(15) = 30 cm

c=2(15)+1=31 cm

Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?

Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?Let k represent Kates age

Kates age = K

Andys age = 2K

Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?

Kates age = K

Andys age = 2K

6 years from now

Kates age = K + 6

Andys age = 2K + 6

Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?

Kates age = K

Andys age = 2K

6 years from now

Kates age = K + 6

Andys age = 2K + 6

In 6 years their ages total 60

K+6+2K+6 = 60

Andy is twice as old as Kate. In 6 years, their ages will total 60. How old is each now?

Kates age = K

Andys age = 2K

6 years from now

Kates age = K + 6

Andys age = 2K + 6

In 6 years their ages total 60

K+6+2K+6 = 60

3K+12=603K=48K=16

Kate = 16 & thereforeAndy=2(16)=32

Find three consecutive numbers whose sum is forty-five.

Find three consecutive numbers whose sum is forty-five.Let n represent the first numberWhats a number??

First number = N

Find three consecutive numbers whose sum is forty-five.Whats a number??

First number = N

Therefore

Second number = N + 1Third number = N + 2

Find three consecutive numbers whose sum is forty-five.Whats a number??

First number = N

Therefore

Second number = N + 1Third number = N + 2

#1+#2+#3 = 45

N+(N+1)+(N+2) =4 5

Find three consecutive numbers whose sum is forty-five.Whats a number??

First number = N

Therefore

Second number = N + 1Third number = N + 2

#1+#2+#3 = 45

N+(N+1)+(N+2) =4 5

Finally3N+3=453N=42N=14

#1=14, #2=15 & #3=16

This carries over to other courses as well as real life scenarios.

We have already seen it at use in science, but what about problems we face in our lives

Lets say you need to buy a NEW XBox 360. You have $800 to spend on everything. You know a new system costs $400 and extra controller $40. Assuming a game costs $60 how many games could you get? Let x= the number of Games $800 = $400 + $40 +$60x 800=460+60x 360=60x x = 6 Games

1. The first side of a triangle is seven cm shorter than twice the second side. The third side is four cm longer than the first side. The perimeter is eighty cm. Find the length of each side.

2. Matt is 3 times as old as Jenny. In 15 years, their ages will total 58. How old is each person now?

3. Find three consecutive even numbers whose sum is 156.

What are four things that a car and a tree have in common?

They have trunksThe could be used for shelterThey give off gassesThey take in gasses

They have trunksThe could be used for shelterThey give off gassesThey take in gasses

. Both hard to eatYou can sit in bothThey could both be green