Transcript English in Math

- Solving equations from word problems
MacDonald
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!

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+
Synonyms are different words with
almost identical or similar meanings
Let’s review some of the words we use in
association with our normal math
operators:
-
x
÷
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Synonyms are different words with
almost identical or similar meanings
Let’s 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
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How do we do it?
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Why are they so hard?
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I just don’t get it!
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Forget it …. I’m done.
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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.
There’s no numbers!

A tongue twister with #s
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.
Trial & Error takes so long
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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?)
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3. Create an equation using the variable(s)
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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.
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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 B
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 = 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 cm
a= 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?
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Andy is twice as old as Kate. In 6 years, their
ages will total 60. How old is each now?
Let k represent Kate’s 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
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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=60
3K=48
K=16
Kate = 16 & therefore
Andy=2(16)=32
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Find three consecutive numbers
whose sum is forty-five.
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
Find three consecutive numbers
whose sum is forty-five.
Let n represent the first number
What’s a number??
First number = N

Find three consecutive numbers
whose sum is forty-five.
What’s a number??
First number = N
Therefore
Second number = N + 1
Third number = N + 2

Find three consecutive numbers
whose sum is forty-five.
What’s a number??
#1+#2+#3 = 45
First number = N
N+(N+1)+(N+2) =4 5
Therefore
Second number = N + 1
Third number = N + 2

Find three consecutive numbers
whose sum is forty-five.
What’s a number??
#1+#2+#3 = 45
First number = N
N+(N+1)+(N+2) =4 5
Therefore
Finally
3N+3=45
3N=42
N=14
Second number = N + 1
Third number = N + 2
#1=14, #2=15 & #3=16
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
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
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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
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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?
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They have trunks
The could be used for shelter
They give off gasses
They take in gasses
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They have trunks
The could be used for shelter
They give off gasses
They take in gasses
…. Both hard to eat
You can sit in both
They could both be green