23.4 Translating Sentences in Equations You already know how to do most of this!Same as section 2.3But a few new add-ons (just a few)
3How do I do these again? 1. Assign a variable to the unknown number 2. Find two verbal expressions for the same value3. write the math expression for each verbal expression4. Write in the equals sign5. Solve it!
4Many words for the same thing The Inuit's have over 20 words for snowWe have 5 ways to say this symbol “=“EqualsIsIs equal toAmounts toRepresents
5How its used Translate “five less than a number is thirteen” The number : nFive less than a number: n-5Thirteen: 13n-5 = 13Or
6Spongebob sez:The sum of two numbers in sixteen. The difference between four times the smaller number and two is two more than twice the larger number. Find those two numbers!
7Smaller number: n Bigger number: 16-n 4n – 2 = 2(16-n) +2 The difference between four times the smaller and twoTwo more than twice the largeIs4n – 2 = 2(16-n) +2
8Example 2: The real world You go into a ritzy night club and it costs $25 for all of you just to get in. In an attempt to impress your date, you decide that you will buy the “beverages*” for the group. Each round of beverages costs you $12 dollars. If your total bill including your entrance fee and all the rounds is $97, how many rounds did you buy?*no alcohol
925 + 12*n = 97 Each round: n $25 entrance fee plus $12 for each round $97is*n = 97
10You Try ItThe sum of two numbers is twenty-five. The total of four times the smaller number and two is six less than the product of two and the larger number. Find the two numbers4x+2=2(25-x)-67,18
11Even, Odd, and consecutive Even integer—a number divisible by 2Like 4Odd integer – a number not divisible by 2Like 5Consecutive integers -- integers that follow one another in orderLike: 101, 102, 103 or -5, -4, -3 or x, x+1, x+2Consecutive even integers: 2, 4, 6 or y, y+2, y+4Consecutive odd integers: 11, 13, 15, or n, n+2, n+4Variable representation is the same for consecutive odd or even why?
12Examples Sum of three consecutive odd integers is 45. Find ‘em. First odd integer: nSecond odd integer: n+2Third odd integer: n+4The sum of these is 45
13You try it NOW!The sum of two numbers is twelve. The total of three times the smaller number and six amounts to seven less than the product of four and the larger numbers. Find the two numbers!5, 7Find three consecutive integers whose sum is negative six-3,-2,-1
14Happy ThanksgivingBeing the great chef you are, you cooked a 20 foot long bird for Thanksgiving. You cut it into two pieces to make it fit on the table. Five times the length of the shorter piece is 2 ft more than twice the length of the longer piece. The length of each piece.
15For difficult problems Draw it out! Shorter piece: xLonger piece: 20 –xThe shorter piece is usually the variable and the longer is the total minus the shorter piece (i.e. what is left).For difficult problems Draw it out!2 ft more than twice the length of the longerFive times the length of the shorter pieceis5x = 2(20 –x) +2
16You try thisA piano wire 24 in. long is cut into two pieces. The longer piece is 4 in. more than three times the shorter piece. Find the length of each piece.5 in., 19 in.An Electric company charges $0.07 for each of the first 249 kWh (kilowatt-hours) and $.14 for each kilowatt-hour over 249 kWh. Find the number of kilowatt-hours used by a family whose electric bill was $28.77330 kwh