LET STATEMENTS Using Addition Subtraction REVIEW 5 Steps

LET STATEMENTS Using Addition & Subtraction REVIEW: 5 Steps to solving word problems: Today we will do all 5 steps…. • Assign labels (“let” statements) • Write a verbal model • Write an algebraic equation • Solve the algebraic equation • Check your answer

Let’s do one from yesterday…. Step 1: ASSIGN LABELS …. we did this yesterday…. . Two consecutive integers have a sum of 93. What are the integers? IMPORTANT…. Let If there are 2 questions… you will have 2 answers! n = first # Let n+1 = second # 93 = sum of #

Step 2: VERBAL MODELS…. also did this yesterday n = first # Let n+1 = second # Let 93 = sum of # first number + second number = sum of numbers

And Step 3 – WRITE AN ALGEBRAIC EQUATION: Let n = first # Just substitute in the values! Let n+1 = second # 93 = sum of # first # n + + second # (n + 1) = sum of # = 93 Now we have an equation!!

And Step 4 – SOLVE THE ALGEBRAIC EQUATION: n + (n + 1) = 93 2 n + 1 = 93 -1 -1 2 n = 92 2 2 n = 46 Combine like terms

SO… n=46. . . BUT WHAT WAS THE QUESTION? ! Two consecutive integers have a sum of 93. What are the integers? Let n = first # Let n+1= second # MS E L B O R P D D R WO D WOR ! !! NEE WERS ANS n = 46 n+1 = If there are 2 questions… you will have 2 answers! 46+1= 47 46 & 47 are consecutive integers!!

And Step 5 – CHECK YOUR ANSWER – 2 ways to choose – but must show work. : Plug in the values of n…MAKE HOLES AND PLUG IN. n + 1 = 93 ( ) + 1 = 93 (46) + 1 = 93 46 + 47 = 93 93 = 93 Can also check into the second step of the equation. . 46 + 47 = 93

Here is another one…A new one! Larry is 8 years older than Sue. Their combined age is 28 years. How old are each of the kids? Step 1: ASSIGN LABELS s =Sue’s age Let s + 8 = Larry’s age Let 28 = combined ages

Step 2: VERBAL MODELS… s =Sue’s age Let s + 8 = Larry’s age Let Words…… 28 = combined ages Sue’s age + Larry’s age = combined ages

And Step 3 – WRITE AN ALGEBRAIC EQUATION: Let s = Sue’s age Let s + 8 = Larry’s age numbers…… 28 = combined ages Sue’s age + Larry’s age = combined age s + (s + 8) = 28

And Step 4 – SOLVE THE ALGEBRAIC EQUATION: Sue’s age + Larry’s age = combined age s + (s + 8) = 28 2 s + 8 = 28 -8 -8 2 s = 20 2 2 s = 10

SO… s=10……. BUT WHAT WAS THE QUESTION? ! What are the ages of Sue and Larry? Let s = Sue’s age Let s+8= Larry’s age s = 10 s+8 = 10+8= If there are 2 questions… you will have 2 answers! 18 Sue is 10 years old and Larry is 18 years old

And Step 5 – CHECK YOUR ANSWER: Here is our original equation…. . plug in the values of s…. s + (s + 8) = 28 ( ) + 8 = 28 ( 10 ) + 8 = 28 20 + 8 = 28 28 = 28 Can also check into the second step of the equation…… 10 + 18 = 28

Last one…. . You want to buy 2 new football jerseys. One is $8 less then the other one. If you paid $38 for both of the jerseys, what did each jersey cost? Step 1: ASSIGN LABELS Let j = price of one jersey Let j - 8 = price of second jersey 38 = cost of both jerseys

And Step 3 – WRITE Step 2: VERBAL MODELS… AN ALGEBRAIC Let j = price of one jersey EQUATION: Let j - 8 = price of second jersey 38 = cost of both jerseys First jersey + Second jersey = total spent j + ( j – 8) = 38

And Step 4 – SOLVE THE ALGEBRAIC EQUATION: First jersey + Second jersey = total cost j + ( j – 8) = 38 2 j – 8 = 38 +8 +8 2 j = 46 2 2 j = 23

SO… j = 23…. BUT WHAT WAS THE QUESTION? ! What is the cost of each jersey? The first jersey cost = j = $23 The second jersey cost = j – 8 = 23 – 8 = $15 And Step 5 – CHECK YOUR ANSWER: j + j – 8 = 38 23 + 23 – 8 = 38 46 – 8 = 38 38 = 38