Algebra Demystified 2nd Ed

258 algebra De mystif ieD

The total amount of money is $1.54, so

02. 50 ... 20 030002 15. 4

(

x +++=xxx

amountin (amountinn(amountin (amountin

quarters)dimes)nickels)pennnies)

025020 030002 154

077154

154

07

. ....
..
.
.

xxxx

x

x

+++=

=

=

77

x= 2

Bobbie has 2 quarters; 2x = 2(2) = 4 dimes; 6x = 6(2) = 12 nickels; and 2x =

2(2) = 4 pennies.

PRACTICE

1. A vending machine as $19.75 in dimes and quarters. There are 100 coins
   in all. How many dimes and quarters are in the machine?


2. Ann has $2.25 in coins. She has the same number of quarters as dimes.
   She has half as many nickels as quarters. How many of each coin does
   she have?


3. Sue has twice as many quarters as nickels and half as many dimes as nick-
   els. If she has a total of $4.80, how many of each coin does she have?

✔SOLUTIONS

1. Let x represent the number of dimes. Then 100 – x is the number of
   quarters. There is 0.10x dollars in dimes and 0.25(100 – x) dollars in
   quarters.
   0100 25 100 19 75
   01025025 19 75
   01

..().

...

.

xx

xx

+−=

+− =

− 55251975

25 25 00

015525

525

015

x

x

x

x

+=

−−

−=−

=−

−

=

.

.

..

.

.

335

There are 35 dimes and 100 – x = 100 – 35 = 65 quarters.

PRACTICE

1. A vending machine as $19.75 in dimes and quarters. There are 100 coins