# Section 3.4.

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Section 3.4

3.4 Translating Sentences in Equations
You already know how to do most of this! Same as section 2.3 But a few new add-ons (just a few)

How do I do these again? 1. Assign a variable to the unknown number
2. Find two verbal expressions for the same value 3. write the math expression for each verbal expression 4. Write in the equals sign 5. Solve it!

Many words for the same thing
The Inuit's have over 20 words for snow We have 5 ways to say this symbol “=“ Equals Is Is equal to Amounts to Represents

How its used Translate “five less than a number is thirteen”
The number : n Five less than a number: n-5 Thirteen: 13 n-5 = 13 Or

Spongebob 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!

Smaller number: n Bigger number: 16-n 4n – 2 = 2(16-n) +2
The difference between four times the smaller and two Two more than twice the large Is 4n – 2 = 2(16-n) +2

Example 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

25 + 12*n = 97 Each round: n \$25 entrance fee plus \$12 for each round
\$97 is *n = 97

You Try It The 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 numbers 4x+2=2(25-x)-6 7,18

Even, Odd, and consecutive
Even integer—a number divisible by 2 Like 4 Odd integer – a number not divisible by 2 Like 5 Consecutive integers -- integers that follow one another in order Like: 101, 102, 103 or -5, -4, -3 or x, x+1, x+2 Consecutive even integers: 2, 4, 6 or y, y+2, y+4 Consecutive odd integers: 11, 13, 15, or n, n+2, n+4 Variable representation is the same for consecutive odd or even why?

Examples Sum of three consecutive odd integers is 45. Find ‘em.
First odd integer: n Second odd integer: n+2 Third odd integer: n+4 The sum of these is 45

You 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, 7 Find three consecutive integers whose sum is negative six -3,-2,-1

Happy Thanksgiving Being 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.

For difficult problems  Draw it out!
Shorter piece: x Longer piece: 20 –x The 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 longer Five times the length of the shorter piece is 5x = 2(20 –x) +2

You try this A 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 \$28.77 330 kwh

Homework 3.4 1 thru 41 EOO 12, 22, 30, 40, 44