Download Using Equations

Algebra
USING EQUATIONS
The equation method is used to solve problems, for example:
Eve thinks of a number, doubles it, adds 5 and gets the answer 11. What was the
number she thought of?
Let the number be  .
If we double it we get 2 .
If we add 5 we have 2 + 5.
This gives the answer 11.
So
2 + 5 = 11.
Now we can solve the equation.
2 = 11 - 5
2 = 6
 = 3
Eve’s number was 3.
A)
Try these questions by making an equation and solving it:
1)
I think of a number, (  ), double it and add 5. The answer is 19.
What was the number?
2)
Holly thinks of a number ( n ), multiplies it by 3 and adds 3. The
answer is 27. What was her number?
3)
Abbie thinks of a number ( m ) , multiplies it by 5 and subtracts 2 .
The answer is 13. What was the number?
4)
Mohammed thinks of a number ( a ), multiplies it by 4 and subtracts
5 . The answer is 31. What was his number?
5)
Faika thinks of a number ( t ), multiplies it by 9 and subtracts 21. The
answer is 24. What is the number?
6)
I have a number ( n ), I multiply it by 12 and add 17. The answer is 65.
What is n ?
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Algebra
You may need to simplify an equation to solve it:
Example:
These angles add up to 180.
a
2a
a + 2a + 30 = 180
collect the a’s
3a + 30 = 180
3a = 180 - 30
3a = 150
a = 50
30
Example 2:
Jamie has  pounds. Ali has 2 pounds more than Jamie. Together they have 28
pounds. How much does Jamie have?
We can only have one unknown, which is  , so we need to describe what Ali has in
terms of . Ali has  + 2 pounds.
So  +  + 2 = 28
2 + 2 = 28
2 = 28 - 2
2 = 26
 = 13
Jamie has 13 pounds.
(Check your answer: that means Ali has £15. £15 + £13 = £28.)
B)
Have a try at solving these problems:
1)
What is angle a ?
2)
2a
These angles add up to 180.
a
60
Ahmed has  pounds.
Jackie has 3 pounds more than Ahmed. Together they have 35 pounds.
How much does Ahmed have?
3)
Angie was on her mobile phone for m minutes. Her brother Nathan was
on for 15 minutes longer than Angie.
Altogether they were using the phone for 53 minutes. How long did
Angie talk for?
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Algebra
4)
Anne Marie has p pounds.
Her sister Danielle has 6 pounds more than Anne Marie.
Their brother David has 2 pounds more than Anne Marie.
Together they have £38. How much does each one have?
5)
Grace spends  pounds.
Leroy spends 3 pounds less than Grace.
Together they spent 41 pounds. How much did they each spend?
6)
Munib has  CDs in his collection.
Frankie has 5 more than Munib.
Leyla has 3 less than Munib.
Together they have 62 CDs. How many does each have?
7)
Bernie gives his children a puzzle: the page number he is on plus the
next 2 page numbers add up to make 72. Let the page number be n
and solve the puzzle.
8)
The angles in this quadrilateral
(4 sided shape) add up to
make 360.
 + 60
Can you form an equation to
work out the value of 
and so find the angles?
80
2
 + 20
Check your answers then discuss with your tutor what you need to work on next.
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Algebra
Answers
Using Equations
A)
B)
1)
2 + 5 =
 =
19
7
2)
3n + 3 =
n =
27
8
3)
5m - 2 =
m =
13
3
4)
4a - 5 =
a =
31
9
5)
9t - 21 =
t =
24
5
6)
12n + 17 =
n =
65
4
1)
3a + 60 =
a =
180
40
2)
2 + 3 =
 =
35
16
Ahmed has 16 pounds.
2m + 15 =
m =
53
19
Angie talked for 19 minutes.
3p + 8 =
p =
38
10
2 - 3 =
 =
41
22
6) 3 + 5 - 3 =
 =
62
20
7)
3n + 3 =
n =
72
23
8)
4 + 160 =
 =
3)
4)
5)
Anne Marie has 10 pounds.
Danielle has 16 pounds.
David has 12 pounds.
Grace spent 22 pounds.
Leroy spent 19 pounds.
Munib has 20 CDs.
Frankie has 25 CDs.
Leyla has 17 CDs.
360
50
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