Systems of Linear Equations Word Problems STEPS Step

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. 10 c + 2. 35 s = 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. 10 c + 2. 35 s = 294. 20 (multiply by 100) 110 c + 235 s = 29420 -110 ( c + s = 172) -110 c – 110 s = -18920 ____________ 125 s = 10500 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 _______ c = 88 Eighty eight cones were sold.

EXAMPLE 2 Your teacher is giving you a test worth 100 points containing 40 questions. There are twopoint 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 fourpoint 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 2 t + 4 f = 100

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) -2 t – 2 f = -80 2 t + 4 f = 100 _______ 2 f = 20 2 2 f = 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 _____ 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