1. Systems of Linear Equations Word Problems

2. 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

3. Example 1
At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold?

4. At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ 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 s = c + s = 172

5. At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold?
STEP 3: Solve the equation using the most convenient method 1.10c s = (multiply by 100) 110c + 235s = ( c + s = 172) -110c – 110s = _______________________ 125s = s = 84

6. At an ice cream parlor, ice cream cones cost $1.10 and sundaes cost $ One day the receipts for a total of 172 cones and sundaes were $ How many cones were sold?
c + s = 172 c + 84 = _____________ c = 88 Eighty eight cones were sold.

7. 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?

8. 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

9. 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?
-2(t + f = 40) -2t – 2f = -80 2t + 4f = 100 ______________ 2f = f = 10

10. 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?
t + f = 40 t + 10 = __________ t= 30 There are thirty (30) 2-point questions on the test and ten (10) 4-point questions on the test.

11. 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

12. 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