Algebra Demystified 2nd Ed

Chapter 8 linear appliCaTionS 245

✔SOLUTIONS

1. Let x = first number, and x + 15 = second number.
   Their sum is 85, so x + (x + 15) = 85.

xx

x

x

x

x

++=

+=

−−

=

=

=

() 15 85

21585

15 15

270

70

2

35

The numbers are 35 and x + 15 = 35 + 15 = 50.

2. Let x = first number and 3x = second number.
   Their sum is 48, so x + 3 x = 48.

xx

x

x

x

+=

=

=

=

348

448

48

4

12

The numbers are 12 and 3(12) = 36.

The relationship between the unknown numbers in the previous problems
was fairly simple. The relationship between the two numbers in the following
problems is less simple, but the strategy is the same.

EXAMPLE

The difference between two numbers is 13. Twice the smaller plus three

times the larger is 129. What are the numbers?

EXAMPLE

The difference between two numbers is 13. Twice the smaller plus three