Algebra Demystified 2nd Ed

248 algebra De mystif ieD

is x + 8. One and a half of the smaller number is 112 x; four times the

larger is 4(x + 8).

11

2

4854

3

2

43254

23

2

432254

xx

xx

xx

++=

++=

 ++







=

()

( ))

23 ()()

2

24 232 108

3864 108

1

xx

xx

















++=

++=

1164 108

64 64

11 44

44

11

4

x

x

x

x

+=

−−

=

=

=

The smaller number is 4 and the larger, x + 8 = 4 + 8 = 12.

4. Let x = smaller number. Then 11 – x is the larger. Five times the smaller
   is 5x, and twice the larger is 2(11 − x). “Twice the larger subtracted from
   five times the smaller” becomes “5x – 2(11 – x).”
   5211 6
   5222 6
   7226
   22 22
   728
   28
   7

xx

xx

x

x

x

x

−−=

−+=

−=

++

=

=

=

()

44

The smaller number is 4 and the larger is 11 − x = 11 − 4 = 7.

Problems Involving Three Unknowns

The problems in this section are a variation of number sense problems. What is

new in this section is that we are given information about three quantities

instead of two. Usually, two of the quantities are compared to a third. We let x

represent the third quantity and write the other two in terms of x.