Equations and Problem
Solving
Using Algebra to solve Word Problems
Counting Problem
and
Mixture Problem
Integers that differ by one. The
integers 50 and 51 are
consecutive and so are -10 and -9
The sum of 3 consecutive integers is 147. Find the integers.
Let n = the first integer
Let n = 48
Then n+1 = the second integer
Then n+1 = 49
And n+2 = the third integer
And n+2 = 50
Consecutive
n
=
147
n + n + 1+ n + 2
=
147
3n + 3
=
147
3n
=
144
n
=
48
+
n+1
+
n+2
The sum of 3 consecutive integers is 72. Find the integers.
Let n = the first integer
Then n+1 = the second integer
And n+2 = the third integer
n
+
n+1
+
n+2
Let n = 23
Then n+1 = 24
And n+2 = 25
=
72
The sum of 3 consecutive integers is 915.
Find the integers.
Let n = the first integer
Then n+1 = the second integer
And n+2 = the third integer
n
+
n+1
+
n+2
Let n = 304
Then n+1 = 305
And n+2 = 306
=
915
Mixture Problem
John has $1.70, all in dimes and nickels.
He has a total of 22 coins. How many of
each kind does he have?
d = dimes n = nickels
Step 1: Assigning variables:
Step 2: Write algebraic equation:
Step 3: Write value equation:
d + n = 22
.10d + .05n = 1.70
Step 3: Write value equation: .10d + .05n = 1.70
Step 4: Solve the mixture problem:
(10)
.10d + .05n = 1.70
(10)
10d
170
.10d + .05n
5n = 1.70
(10)
d +
n =
22
10d
220
.10d + .05n
10n = 1.70
(10)
Step 4: Solve the mixture problem:
10d + 5n = 170
10d +
220
-10d
- 10n = -220
Change the sign of
the 2nd equation
-5n
10n = 220
-50
-5
-5
n = 10
10d + 5n = 170
10d + 5(10) = 170
10d + 50
-50
10d
d
= 170
-50
= 120
= 12
Warm-up
1. The sum of 3 consecutive integers is 60.
What are the values of the 3 integers?
1. The 3 consecutive numbers
are 29, 30 and 31.
Mixture Problem
Tickets to a movie cost $5.00 for adults and $3.00 for
children. If tickets were bought for 50 people for a
total of $196 how many adult tickets were sold and
how many children tickets were sold?
Step 1: Assigning variables:
Step 2: Write algebraic equation:
Step 3: Write value equation:
a = adults c = children
a + c = 50
5a + 3c = 196
5a + 3c = 196
Step 3: Write value equation:
Step 4: Solve the mixture problem:
(-5)
a
+
c
=
50
(-5)
-5a
-250
-5a - 5c
-5c= -250
5a + 3c = 196
-2c = -54
-2
-2
c = 27
-5a - 5c = -250
-5a - 5(27)= -250
-5a - 135 = -250
+ 135
-5a
a
+ 135
= -115
= 23
Mixture Problem
Tickets to a movie cost $4.00 for adults and $2.00 for
children. If tickets were bought for 80 people for a
total of $230 how many adult tickets were sold and
how many children tickets were sold?
c = 45
a
= 35
Your homework
Amy has 32 coins consisting of dimes
and quarters. If Amy has a total of $5 in
her pocket, how many of each coin are
there?
Dimes = 20
Quarters = 12