There are two ways to do these problems.
(1) using only 1 unknown
(2) using 2 unknowns.
I will assume you are studying using 2 unknowns.
If you have not gotten to using 2 unknowns yet,
then tell me in the thank you note and I'll show
you how to do these using only one unknown.
1. Ron has 30 coins with a total value of $5.25.
The coins are dimes and quarters. How many of
each coin does he have?
how value of value of
many each all
dimes x .10 .10x
quarters y .25 .25y
-----------------------------------------
totals 30 5.25
x+y=30 .10x+.25y=5.25
Solve first equation for x
x=30-y
Substitute in second equation
.10(30-y)+.25y = 5.25
3.00-.10y+.25y = 5.25
3.00+.15y = 5.25
.15y = 2.25
y = 2.25/.15
y = 15 quarters
Substitute in x = 30-y
x = 30-15
x = 15 dimes
Checking: 15 quarters = $3.75
15 dimes = 1.50
total $5.25
2. Ron has 15 coins with a total value of $1.95. The
coins are nickels and quarters. How many of each
coin does he have?
how value of value of
many each all
nickels x .05 .05x
quarters y .25 .25y
-----------------------------------------
totals 15 1.95
x+y=15 .05x+.25y=1.95
Same as above. Get 9 nickels and 6 quarters
3. How many liters of 80% alcohol solution and 20%
alcohol solution must be mixed to obtain 6 liters
of 40% alcohol solution?
how much
how percent pure
much alcohol alcohol
liquid in each in each
stronger x .80 .80x
weaker y .20 .20y
-----------------------------------------
totals 6 .40 .40(6)
x+y=6 .80x+.20y=.40(6)
.80x+.20y= 2.4
Same way, get x=2, y=4
Edwin
