Objective - To solve various problems
using systems of linear equations.
We will be studying 3 types of problems
1) Number and Value Problems
2) Mixture Problems
3) Comparison Problems
Number and Value Problem #1
Joe bought 15 items for $135. If the 15 items
consisted of notebooks that cost $4.50 each and
calculators that cost $12.00 each, how many of
each did he buy?
Let x = # of notebooks Let y = # of calculators
x
x
y
y
y
y
15
15
y
9
15
x
15
x
6
6 notebooks
4.5x
x
4.5x
4 .5 x
12 y
135
12 15
x
135
180
180
12 x
135
180
45
7 .5
7 .5 x
7 .5
& 9 calculators
x
6
Number and Value Problem #2
Merna raised $24 by selling 40 baked items for
the Builders Club. She sold cookies for 50 cents
each and brownies for 75 cents each . How many
of each did she sell?
Let c = # of cookies
Let b = # of brownies
50 (c
b
50 c
75 b
c
c
40)
2400
b
40
16
16
40
16
c
24
50 c
50 c
50 b
75 b
2400
25 b
25
400
25
b
24 cookies
2000
16
& 16 brownies
Mixture Problem #1
A 12 pound mixture of peanuts and cashews sells
for $6.50/lb. If peanuts sell for $3 per pound and
cashews sell for $8 per pound, how many pounds
of peanuts are in the mix?
Let p = peanuts (in lbs.) Let c = cashews(in lbs.)
3( p
c
3p
8c
p
p
c
12)
3p
3c
6.5 12
3p
8c
78
5c
5
c
42
5
8 .4
12
8.4
8 .4
12
8 .4
p
3.6
36
3.6 lbs. peanuts
8.4 lbs. cashews
&
Mixture Problem #2
A 10% acid solution is mixed with a 60% acid
solution to produce 120 liters of a solution that
is 40% acid. How much of each solution was
used to create the mixture?
Let x = liters of 10% sol. Let y = liters of 60% sol.
x y 120
y 120 x
.10 x .60 y .40 (120 )
y 120 48
.10 x .60 120 x
48
y 72
.10 x
72
72
.60 x
.50 x
.50
x
48
72
24
.50
48
48 L 10% Sol.
&
72 L 60% Sol.
Comparison Problem
The population of Clinton is 50,000 but is
growing at 2500 people per year. Oak Valley
has a population of 26,000 but is growing at
4000 people per year. When will both towns
have equal population.
Let x = # of years
Let p = population
Clinton
Oak Valley
p
50, 000
50, 000
2500 x
p
26, 000
4000 x
2500 x
26, 000
50, 000
26, 000
24 ,000
26, 000 1500 x
26, 000
1500 x
in 16 years
x
2500 x
16
4000 x
2500 x