Systems of Linear Equations Word Problems

1. Systems of Linear EquationsWord 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 $2.35. One day the receipts for a total of 172 cones and sundaes were $294.20. How many cones were sold?

4. 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

5. 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

6. 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.

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= 20 2 2 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= 40 -10 -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