1. Writing Two-Step Equations

2. Equation – a mathematical sentence containing variables, numbers and operation symbols Two-step equation – an equation with a combination of: multiplication or division with addition or subtraction

3. Keywords Is, was: equal Increased by: + More than: + Decreased by: - Less: - Less than: - The product of: ( ) Twice: 2 Triple: 3 The quotient of: ÷

4. The product of a number and four increased by seven is thirty-one. 4x + 7 = 31 + -7 + -7 4x = 24 4 4 x = 6 Mrs. Copple’s father is 71 years old. This is thirty- one less than six times Mrs. Copple’s son’s age. Find my son’s age. 6a – 31 = 71 +31 +31 6a = 102 6 6 a = 17

5. The quotient of a number and negative five less twelve is negative one. n - 12 = -1 -5 + 12 +12 (-5) n = 11 (-5) -5 n = -55 Nineteen less than a number divided by two is thirty. x - 19 = 30 2 +19 +19 2 x = 49 2 2 x = 98

6. Jill earns $8 an hour for babysitting plus a $5 tip. Last night Jill earned $37. How many hours did she babysit? 8h + 5 = 37 -5 -5 8h = 32 8 8 h = 4 Sam had a certain number of baseball cards (c). He split then evenly among his two brothers. Sam’s friend gave him 15 more for his birthday. If Sam would have had 65 cards after his friend gave him some, before splitting them among his brothers, how many cards did Sam have in the beginning? c + 15 = 65 2

7. 331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were on each bus? 6b + 7 = 331 - 7 - 7 6b = 324 6 6 b = 54 Alice had $24 to spend on seven pencils. After buying them, she had $10. How much did each pencil cost? 7p + 10 = 24 - 10 - 10 7p = 14 7 7 p = 2

8. Maria bought seven boxes. A week later, half of all of her boxes were destroyed in a fire. There are now 22 boxes left. How many did she have in the beginning? b + 7 = 22 2 - 7 - 7 b = 15 2 b = 30 Ian spent half his weekly allowance playing mini-golf. To earn more money, his parents let him wash the car for $4. What is his weekly allowance if he ended with $12? a + 4 = 12 2 - 4 - 4 a = 8 2 a = 16

9. How old an I if 400 reduced by 2 times my age is 244? 400 – 2a = 244 400 + (-2a) = 244 - 400 - 400 -2a = -156 -2 - 2 a = 78 The Cooking Club made some pies to sell at a basketball game to raise money. The cafeteria contributed four pies to the sale. Each pie was then cut into five pieces and sold. There were a total of 60 pieces to sell. How many pies did the club make? p + 20 = 60 5 - 20 - 20 p = 40 5 p = 200

10. Joe’s father is 45. He is 15 years older than twice Joe’s age. How old is Joe? 2j + 15 = 45 - 15 - 15 2j = 30 2 2 j = 15 Your mother took you shopping this weekend. She purchased jeans and shirts. The jeans cost $45 each and the shirts cost $25 each. If she bought twice as many shirts as jeans, and spent $190 on you, how many jeans and how many shirts did she buy? 45j + 2(25j) = 190 45j + 50j = 190 jeans = 2 shirts = 4

11. On a prealgebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. What was the lowest grade? g + g + 42 = 138 2g + 42 = 138 - 42 - 42 2g = 98 2 2 g = 49 Jamie drove twice as far as Rhonda. Together, they drove 90 miles. Find the number of miles driven by each girl. Let ‘m’ stand for Jamie’s miles. Let ‘2m’ stand for Rhonda’s miles. m + 2m = 90 3m = 90 3 3 m = 30

12. The length of a rectangular map is 15 inches. The perimeter of the map is 50 inches. Find the width. P = l + w + l + w P = 2(l + w) 50 = 2(15 + w) 50 = 30 + 2w -30 -30 20 = 2w 2 2 10 = w Jose has a board that is 44 inches long. He wants to cut it into two pieces so that one piece is six inches longer than the other. How long should the shorter piece be? Let ‘p’ be the shorter piece. Let ‘p + 6’ be the longer piece. p + p + 6 = 44 2p + 6 = 44 - 6 - 6 2p = 38 2 2 p = 19 shorter = 19” longer = 25”