Algebra Demystified 2nd Ed

246 algebra De mystif ieD

If the difference between two numbers is 13, then one of the numbers is

13 more than the other. As before, we let x represent the first number. Then,

x + 13 represents the other. “Twice the smaller” means “2x” (x is the smaller

quantity because the other quantity is 13 more than x). Three times the

larger number is 3(x + 13). “Twice the smaller plus three times the larger is

129” becomes the equation 2x + 3(x + 13) = 129.

2313 129

2339 129

539 129

39 39

590

xx

xx

x

x

x

++=

++=

+=

−−

=

()

==

=

90

5

x 18

The numbers are 18 and x +13 = 18 + 13 = 31.

The sum of two numbers is 14. Three times the smaller plus twice the larger

is 33. What are the two numbers?

We let x represent the smaller number. How can we represent the larger

number? We know that the sum of the smaller number and larger number

is 14. Let “?” represent the larger number and we’ll find “?” in terms of x.

The smaller number plus the larger number is 14.

x +? = 14

We solve this “equation” for the “?” symbol.

x

xx

x

+=

−−

=−

?

?

14

14

So, 14 – x is the larger number. Three times the smaller is 3x. Twice the larger

is 2(14 – x). Their sum is 33, giving us the equation 3x + 2(14 – x) = 33.

3214 33

3282 33

28 33

28 28

5

xx

xx

x

x

+−=

+−=

+=

−−

=

()

The smaller number is 5 and the larger is 14 – x = 14 – 5 = 9.