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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