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 value x + 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 number x + 10 = the first number 2(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 18 second number is 8 third 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 number x/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 now 4x = man's age now {man is 4 times as old as daughter} x + 16 = daughter in 16 years 4x + 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 now x + 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 now Brenda is 12 now Carol is 24 now