The algebra of maths

Equations Solving problems: x + x + 1= 43 2x +1 -1 = 43 – 1 2x = 42 2 2 Solution: x = 21

1) Jack won 71 lollipops playing basketball at country fair 1) Jack won 71 lollipops playing basketball at country fair. At school he gave three to every student in this math class. He only has 5 remaining. How many children are in his class? 71 – 3x = 5 71 – 3x -71 = 5 – 71 -3x = - 66 -3x / (-3)= -66 / (-3) x = 22 There are 22 children.

2) The sum of three consecutive even numbers is 72 2) The sum of three consecutive even numbers is 72. What is the smallest of these numbers? 2x + 2x + 2 + 2x + 4 = 72 6x + 6 = 72 6x + 6 – 6 = 72 – 6 6x = 66 6x / 6 = 66 / 6 X = 11 The smallest number is 22.

3) Brenda have 23$ to spend on two notebooks 3) Brenda have 23$ to spend on two notebooks. After buying them she had 19$. How much did each notebook cost? 2x + 19 = 23 2x + 19 – 19 = 23 – 29 2x / 2 = 4 / 2 X = 2 Each notebook cost 2 $.

4) Jose sold half of his books and then bought twenty more 4) Jose sold half of his books and then bought twenty more. He now has 30. With how many books did he begin? x/2 +20= 30 x/2 = 10 x = 10 · 2 X = 20 He began with 20 books

5) Willie had some paper with which to make not cards 5) Willie had some paper with which to make not cards. On his way to his room he found four more pieces to use. In his room he cut each piece of paper in half. When he was done he had 24 half-pieces of paper. With how many sheets of paper did he start? (x + 4) ·2 = 24 2x + 8 = 24 2x / 2 = 16 / 2 x = 8 He started with 8 papers.

6) Amanda spent half of her weekly allowance on clothes 6) Amanda spent half of her weekly allowance on clothes. To earn more money her parents let her clean the gutters for 8$. What is her weekly allowance if she ended whith 17$? x/2 + 8 = 17 (x/2 + 8) · 2 = 17·2 x + 16 = 34 x = 18 Her weekly allowance is $18.

7) Castel had some candy to give to his three children 7) Castel had some candy to give to his three children. He first took nine pieces of himself and then evenly dicided the rest among his children. Each child received four pieces. With how many pieces did he start? (x – 9)/ 3 = 4 x - 9 = 4.3 X= 12 +9 = 27 Castel had 27 candies

8) Kristin bought eight boxes 8) Kristin bought eight boxes. A week later half of all her boxes were destroyed in a fire. There are now only 17 boxes left. With how many did he start? (x + 8) /2 = 17 2x + 16 = 34 2x/2 = 18/2 x = 9 He started with 9 boxes.

9) Matt rented a bike from Jessica’s Bikes 9) Matt rented a bike from Jessica’s Bikes. It cost 13$ plus 4$ per hour. If Matt paid 37$ then he rented the bike for how many hours? 4x + 13 = 37 4x + 13 – 13 = 37 – 13 4x / 4 = 24 / 4 x = 6 He rented the bike for 6 hours.

10) How old I am if reduced by 2 times my age is 18 10) How old I am if reduced by 2 times my age is 18? 200 – 2x = 18 -2x = 18 – 200 -2x/2 = -182 /2 X = 91 I am 91 years old.

THE END By : Chiara Rdguez Diaz.