Systems of
Linear
Equations
Word Problems
STEPS
 Step
1: Define your variables
 Step 2: Write a system of linear equations
 Step 3: Solve the system for each variable
using the most convenient method
 Step 4: Check for reasonableness
Example 1
At an ice cream parlor, ice cream
cones cost $1.10 and sundaes cost
$2.35. One day the receipts for a
total of 172 cones and sundaes were
$294.20. How many cones were sold?
At an ice cream parlor, ice cream cones cost
$1.10 and sundaes cost $2.35. One day the
receipts for a total of 172 cones and sundaes
were $294. 20. How many cones were sold?
STEP 1: Define your variables:
Let c = the number of cones sold
Let s = the number of sundaes sold
STEP 2: Write your system of equations
1.10c + 2.35s = 294.20
c + s = 172
At an ice cream parlor, ice cream cones cost
$1.10 and sundaes cost $2.35. One day the
receipts for a total of 172 cones and sundaes
were $294.20. How many cones were sold?
STEP 3: Solve the equation using the most
convenient method
1.10c + 2.35s = 294.20 (multiply by 100)
110c + 235s = 29420
-110 ( c + s = 172)
-110c – 110s = -18920
_______________________
125s = 10500
125
125
s = 84
At an ice cream parlor, ice cream cones cost
$1.10 and sundaes cost $2.35. One day the
receipts for a total of 172 cones and sundaes
were $294. 20. How many cones were sold?
c + s = 172
c + 84 = 172
-84 -84
_____________
c = 88
Eighty eight cones were sold.
EXAMPLE 2
Your teacher is giving you a test worth 100
points containing 40 questions. There are
two-point and four-point questions on the
test. How many of each type of question
are on the test?
Your teacher is giving you a test worth 100 points
containing 40 questions. There are two-point and
four-point questions on the test. How many of
each type of question are on the test?
STEP 1:
Let t = the number of 2 point questions
Let f = the number of 4 point questions
STEP 2:
t + f = 40
2t + 4f = 100
Your teacher is giving you a test worth 100 points
containing 40 questions. There are two-point and fourpoint questions on the test. How many of each type of
question are on the test?
-2(t + f = 40)
-2t – 2f = -80
2t + 4f = 100
______________
2f = 20
2
2
f = 10
Your teacher is giving you a test worth 100 points
containing 40 questions. There are two-point and fourpoint questions on the test. How many of each type of
question are on the test?
t + f = 40
t + 10 = 40
-10 -10
__________
t= 30
There are thirty (30) 2-point questions on the
test and ten (10) 4-point questions on the
test.
EXAMPLE 3 (You Try)
The sum of two numbers is 24. Their
difference is 15. What are the two numbers?
 Step 1: Define your variables
 Step 2: Write a system of linear equations
 Step 3: Solve the system for each variable
using the most convenient method
 Step 4: Check for reasonableness
EXAMPLE 4 (You Try)
Mac’s wallet is full of $5 and $10 bills. He has
25 bills totaling $230. How many of each bill
does he have?
 Step 1: Define your variables
 Step 2: Write a system of linear equations
 Step 3: Solve the system for each variable
using the most convenient method
 Step 4: Check for reasonableness