Algebra Demystified 2nd Ed

56 algebra De mystif ieD

deMYstiFied / algebra deMYstiFied / HuttenMuller / 000-0 / Chapter2

3.^34
25

325

25

4

25

75

25

4

25

75 4

xx 25

x

xx

x

x

x

x

+=⋅+⋅= +=+

4.^2
45

6

35

2

45

7

7

6

35

9

9

14

315

54

315

14 54

xx

x

xx

x

x

+= ⋅+ ⋅= +=+ x

3315 x

5.^11
150

7

36

11

150

6

6

7

36

25

25

66

900

175

xx 900

x

xx

x

x

+= ⋅+ ⋅= + ==^66 +^175

900

x

x

6.^2
21

3

98

2

21

14

14

3

98

3

3

28

294

9

294

37

xxxxxx 294 x

+=⋅+ ⋅= +=

7.^1
12

5

9

1

12

3

3

5

9

4

4

3

36

20

36

32

xy x

y

yy

x

x

y

xy

x

xy

+=⋅+⋅= +=y+^00

36

x

xy

8.^19
51

1

6

19

51

2

2

1

6

17

17

38

102

17

yxy 102

x

xx

y

y

x

xy

−=⋅−⋅= − y

xxy

xy

xy

=^38 −^17

102

9.^7
24

2

15

7

24

5

5

2

15

8

8

35

120

16

120

x 35

yy

x

yy

x

yy

+=⋅+ ⋅= +=x+^116

120 y

10.^3
14

2

35

3

14

5

5

2

35

2

2

15

70

4

70

15

yxy

x

xx

y

y

x

xy

y

xy

+=⋅+ ⋅= +=xxy

xy

+ 4

70

Variables in Word Problems

Often the equations used to solve word problems should have only one variable, so

other unknowns must be written in terms of a single variable. The goal of this sec-

tion is to acquainte you with setting the variable equal to an appropriate unknown

quantity and writing other unknown quantities in terms of the variable.

EXAMPLES

Andrea is twice as old as Sarah.

Because Andrea’s age is being compared to Sarah’s, the easiest thing to

do is to let x represent Sarah’s age:

Let x = Sarah’s age.

Andrea is twice as old as Sarah, so Andrea’s age = 2x. We could have let

x represent Andrea’s age, but we would have to re-think the statement

as “Sarah is half as old as Andrea.” This would mean Sarah’s age would

be represented by^12 x.

EXAMPLES

Andrea is twice as old as Sarah.