3Problem of the DayYou buy 1 cookie on the first day, 2 on the second day, 3 on the third day, and so on for 10 days. Your friend pays $10 for a cookie discount card and then buys 10 cookies at half price. You both pay the same total amount. What is the cost of one cookie?$0.20
4Sunshine State Standards Preview of MA.912.A.3.1 Solve linear equations in one variable that include simplifying algebraic equations.
5Additional Example 1: Using Inverse Operations to Group Terms with Variables Group the terms with variables on one side of the equal sign, and simplify.A. 60 – 4y = 8y60 – 4y = 8y60 – 4y + 4y = 8y + 4yAdd 4y to both sides.60 = 12ySimplify.B. –5b + 72 = –2b–5b + 72 = –2b–5b + 5b + 72 = –2b + 5bAdd 5b to both sides.72 = 3bSimplify.
6Check It Out: Example 1Group the terms with variables on one side of the equal sign, and simplify.A. 40 – 2y = 6y40 – 2y = 6y40 – 2y + 2y = 6y + 2yAdd 2y to both sides.40 = 8ySimplify.B. –8b + 24 = –5b–8b + 24 = –5b–8b + 8b + 24 = –5b + 8bAdd 8b to both sides.24 = 3bSimplify.
7Additional Example 2A: Solving Equations with Variables on Both Sides Solve.7c = 2c + 557c = 2c + 557c – 2c = 2c – 2c + 55Subtract 2c from both sides.5c = 55Simplify.5c = 555Divide both sides by 5.c = 11
8Additional Example 2B: Solving Equations with Variables on Both Sides Solve.49 – 3m = 4m + 1449 – 3m = 4m + 1449 – 3m + 3m = 4m + 3m + 14Add 3m to both sides.49 = 7m + 14Simplify.49 – 14 = 7m + 14 – 14Subtract 14 fromboth sides.35 = 7m35 = 7m7Divide both sides by 7.5 = m
9Additional Example 2C: Solving Equations with Variables on Both Sides Solve.25x =1x– 122515x =x– 1225x15–=1– 1215Subtractx from bothsides.15x–12=Simplify.15(5)x=(5)(–12)Multiply both sides by 5.x = –60
10Check It Out: Example 2ASolve.8f = 3f + 658f = 3f + 658f – 3f = 3f – 3f + 65Subtract 3f from both sides.5f = 65Simplify.5f = 655Divide both sides by 5.f = 13
11Check It Out: Example 2BSolve.54 – 3q = 6q + 954 – 3q = 6q + 954 – 3q + 3q = 6q + 3q + 9Add 3q to both sides.54 = 9q + 9Simplify.54 – 9 = 9q + 9 – 9Subtract 9 from both sides.45 = 9q45 = 9q9Divide both sides by 9.5 = q
12Check It Out: Example 2CSolve.23w =1w– 92313w =w– 91323w13–=1– 9Subtractw from bothsides.13w–9=Simplify.13(3)w=(3)(–9)Multiply both sides by 3.w = –27
13Additional Example 3: Consumer Math Application Christine can buy a new snowboard for $ She will still need to rent boots for $8.50 a day. She can rent a snowboard and boots for $18.25 a day. How many days would Christine need to rent both the snowboard and the boots to pay as much as she would if she buys the snowboard and rents only the boots for the season?
14Additional Example 3 Continued Let d represent the number of days.18.25d = dSubtract 8.5dfrom both sides.18.25d – 8.5d = d – 8.5d9.75d = 136.5Simplify.9.75d = 136.5Divide both sides by 126.96.36.1999.75d = 14Christine would need to rent both the snowboard and the boots for 14 days to pay as much as she would have if she had bought the snowboard and rented only the boots.
15Check It Out: Example 3A local telephone company charges $40 per month for services plus a fee of $0.10 a minute for long distance calls. Another company charges $75.00 a month for unlimited service. How many minutes does it take for a person who subscribes to the first plan to pay as much as a person who subscribes to the unlimited plan?
16Check It Out: Example 3 Continued Let m represent the number of minutes.75 = mSubtract 40from both sides.75 – 40 = 40 – m35 = 0.10mSimplify.m0.10=Divide both sides by 0.10.350 = mA person who subscribes to the first plan would have to use 350 minutes to pay as much as a person who subscribes to the unlimited plan.
17Lesson QuizzesStandard Lesson QuizLesson Quiz for Student Response Systems
18Lesson Quiz: Part IGroup the terms with variables on one side of the equal sign, and simplify.1. 14n = 11n + 812. –14k + 12 = –18kSolve.y = –4y – 194. –3n = 814k = –12y = –113418x =x – 14x = 16
19Lesson Quiz Part II5. Mary can purchase ice skates for $57 and then pay a $6 entry fee at the ice skating rink. She can also rent skates there for $3 and pay the entry fee. How many times must Mary skate to pay the same amount whether she purchases or rents the skates?19 times
20Lesson Quiz for Student Response Systems Group the terms with variables on one side of the equal sign, and simplify.19p = 10p + 54A. 9p = –54B. 29p = –54C. 29p = 54D. 9p = 54
21Lesson Quiz for Student Response Systems 2. Solve.73 + 4m = –7m – 26A. m = –9B. m = –7C. m = 9D. m = 7
22Lesson Quiz for Student Response Systems 3. Matthew orders T-shirts from an online store for $25 each and an additional $20 for shipping. Mike buys the same kind of T-shirts at a local shop for $27 each. If Matthew and Mike spent the same amount, how many T-shirts did each of them buy?A. 5 T-shirtsB. 10 T-shirtsC. 15 T-shirtsD. 20 T-shirts