Algebra Demystified 2nd Ed

Chapter 8 linear appliCaTionS 257

EXAMPLE
Terri has $13.45 in dimes and quarters. If there are 70 coins in all, how many
of each type does she have?

Let x represent the number of dimes. Because the number of dimes and
quarters is 70, 70 – x represents the number of quarters. Terri has x dimes,
so she has $0.10x in dimes. She has 70 – x quarters, so she has $0.25(70 – x)
in quarters. These two amounts must sum to $13.45.
01 .. 00 xx+=25 70() . 13 45
(amountin
dimes)

(amount

−

in

quarters)

0100 25 70 13 45

010175 0

..().

..

xx

x

+−=

+−...

...

..

.

25 13 45

015175 13 45

1751750

015

x

x

x

=

−+=

−−

−=− 4405

405

015

27

.

.

.

x

x

=−

−

=

Terri has 27 dimes and 70 – x = 70 – 27 = 43 quarters.

Bobbie has $1.54 in quarters, dimes, nickels, and pennies. He has twice as
many dimes as quarters and three times as many nickels as dimes. The
number of pennies is the same as the number of dimes. How many of each
type of coin does he have?

Nickels are being compared to dimes, and dimes are being compared to
quarters, so we will let x represent the number of quarters. Bobbie has
twice as many dimes as quarters, so 2x is the number of dimes he has. He
has three times as many nickels as dimes, namely triple 2x: 3(2x) = 6x. He
has the same number of pennies as dimes, so he has 2x pennies.

How much of the total $1.54 does Bobbie have in each coin? He has x quar-
ters, each worth $0.25, so he has a total of 0.25x (dollars) in quarters. He
has 2x dimes, each worth $0.10; this gives him 0.10(2x) = 0.20x (dollars) in
dimes. Bobbie has 6x nickels, each worth $0.05. The total amount of money
in nickels, then, is 0.05(6x) = 0.30x (dollars). Finally, he has 2x pennies, each
worth $0.01. The pennies count as 0.01(2x) = 0.02x (dollars).

EXAMPLE
Terri has $13.45 in dimes and quarters. If there are 70 coins in all, how many