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Consecutive Numbers 1 +1 2 +1 3 +1 4 n n+1 n+2 n+3

Consecutive Numbers 1 +1 2 +1 3 +1 4 n n+1 n+2 n+3 Even Consecutive Numbers 2 +2 4 +2 6 +2 8 n n+2 n+4 n+6 Odd Consecutive Numbers 1 +2 3 +2 5 +2 7

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Consecutive Numbers 1 +1 2 +1 3 +1 4 n n+1 n+2 n+3

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  1. Consecutive Numbers 1 +1 2 +1 3 +1 4 n n+1 n+2 n+3 Even Consecutive Numbers 2 +2 4 +2 6 +2 8 n n+2 n+4 n+6 Odd Consecutive Numbers 1 +2 3 +2 5 +2 7 n n+2 n+4 n+6

  2. Number Word Problems Hints • Represent the first number by a variable, “n” • When finding the sum of consecutive even or consecutive odd integers, you are always adding by 2’s.

  3. The sum of two values is 53. One value is 3 more than the other. What is the larger of the two values? x = one valuex + 3 = other value  {one is three more than the other} x + x + 3 = 53 {sum of the two values is 53}2x + 3 = 53 {combined like terms}2x = 50 {subtracted 3 from each side}x = 25 {divided each side by 2}x + 3 = 28 {substituted 25, in for x, into x + 3} 28 is the larger of the two values

  4. The sum of three numbers is 62  . The first number is 10 more than the second.  The third number is 2 times the first.  What are the numbers? x = the second numberx + 10 = the first number2(x + 10) = the third number x + x + 10 + 2(x + 10) = 62 {sum of the three numbers is 62}x + x + 10 + 2x + 20 = 62 {used distributive property}4x + 30 = 62 {combined like terms}4x = 32 {subtracted 30 from each side}x = 8 {divided each side by 4}x + 10 = 18 {substituted 8, in for x, into x +  10}2(x + 10) = 36 {substituted 8, in for x, into 2(x + 10)} first number is 18second number is 8third number is 36

  5. The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number? x = larger numberx/6 = smaller number {the smaller number is 1/6th the larger number}x - x/6 = 25 {difference of the two numbers is 25}6x - x = 150 {multiplied entire equation by 6 to eliminate fraction}5x = 150 {combined like terms}x = 30 {divided each side by 5}x/6 = 5 {substituted 30, in for x, into x/6} the smaller number is 5

  6. Age Word Problems When solving age problems, you need to represent the following in terms of a variable: • the present ages of the people or things involved • the age, at the other specified time, of the people or things involved • then, form an equation based on these representations

  7. A man is 4-times as old as her daughter.  After 16-years, he will be twice as old as his daughter.  Find the daughter’s age. x = daughter's age now4x = man's age now {man is 4 times as old as daughter}  x + 16 = daughter in 16 years4x + 16 = man in 16 years  4x + 16 = 2(x + 16) {after 16 years, he will be twice as old as her}4x + 16 = 2x + 32 {used distributive property}4x = 2x + 16 {subtracted 16 from both sides}2x = 16 {subtracted 2x from both sides}x = 8 {divided both sides by 2}4x = 32 {substituted 8, in for x, into 4x}  x = 8 {divided both sides by 4}daughter is 8 

  8. If three times Kathy's age is decreased by 36, the result is twice Kathy's age. How old is Kathy? x = Kathy's age 3x - 36 = 2x   {three times her age minus 36 equals twice her age}-36 = -x  {subtracted 3x from both sides}x = 36   {divided both sides by -1} Kathy is 36

  9. Brenda is 4 years older than Walter, and Carol is twice as old as Brenda. Three years ago, the sum of their ages was 35.  How old is each now?  x = Walter's age nowx + 4 = Brenda's age now {Brenda is 4 yrs older than Walter}2(x + 4) = 2x + 8 = Carol's age now {Carol is twice as old as Brenda, used distributive property} x - 3 = Walter's age 3 years ago   {subtracted 3 from x}x + 1 = Brenda's age 3 years ago   {subtracted 3 from x + 4}2x + 5 = Carol's age 3 years ago   {subtracted 3 from 2x + 8} (x - 3) + (x + 1) + (2x + 5) = 35   {sum of ages, 3 years ago, was 35}x - 3 + x + 1 + 2x + 5 = 35   {took out parentheses}4x + 3 = 35   {combined like terms}4x = 32   {subtracted 3 from both sides}x = 8 = Walter now   {divided both sides by 4}x + 4 = 12 = Brenda now   {substituted 8, in for x, into x + 4}2(x + 4) = 24 = Carol now   {substituted 8, in for x, into 2(x + 4)} Walter is 8 nowBrenda is 12 nowCarol is 24 now 

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