Unit 5 - Linear equations exercises and word problems 11/12

Colegio Nuestra Señora del Prado (Ciudad Real) Matemáticas 2ESO

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UNIT 5 LINEAR AND QUADRATIC EQUATIONS

A) LINEAR EQUATIONS

A-1) Linear equations without brackets

A-2) Linear equations with brackets


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A-3) Linear equations with fractions

A-4) Linear equations with brackets and fractions


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SOLUCIONES

1) 10 9) No tiene solución

2) 5 10) 1

3) -2 11) 1

4) 3

2 12) -2

5) 2

1 13) 5

8

6) 5

1 14) 2

17

7) 4 15) Infinitas soluciones

8) -5

16) 1 22) Infinitas soluciones

17) -8 23) 3

18) 4 24) No tiene solución

19) 3

1 25) 2

1

20) -3 26) 4

3

21) 0 27) 12

7

28) 6 38) 3

29) 5 39) Infinitas

30) 9 40) 4

1

31) 2 41) -2

32) 5 42) 3

33) 2 43) 7

34) 2

3 44) -25

35) 2 45) 11

36) No tiene solución 46) 1

37) 8

5 47) 1

48) 3

5

49) 4

5

50) 2

1

51) -4

52) 4

53) -3

54) 4

3

55) 5


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B) LINEAR AND QUADRATIC EQUATIONS – WORD PROBLEMS

1. A number and the number before it add up to 77. What is the number? 39

2. When we add 13 units to the double of a number, the result is 99. What is the number? 43

3. A pride of lions is made up of 13 lions, and there are 3 females more than males. How many lions

and how many lionesses are there in the pride? 5 and 8

4. There are 31 people in a café. How many men and women are there if we know that there are 5

more men than women? 18 and 13

5. In a cow farm, the number of horns and legs add up to 30. How many cows are there in the farm?

5

6. An ice-cream costs 80 cents more than a cake. Kate and George had 1 ice-cream and 2 cakes for

tea, and it all costs 4.40 euros. How much a cake cost? And how much is an ice-cream? 1,2 and 2

7. Calculate the dimensions of a rectangular field, knowing that its length is 20 meters more its width

and that there is a fence which is 240 meters long. 50 and 70

8. The sum of the square of a number and six times the number is 91. Find the two possible values of

the number. -7 and -13

9. Arthur has a bag containing 28 candies, some of them are mints and some others are lemon. If the

number of mints is three times the number of lemon ones, how many candies of each kind can Arthur

eat? 7 lemon and 21 mint

10. John kept 4/5 of the oranges that were in a box. Mary took half of the oranges that were left in

the box, leaving only 5 oranges. How many oranges did the box contain originally? 50

11. Phillip is three years older than his sister Rose. Their combined age is 37. How old are Phillip

and Rose? Phillip 20 and Rose 17

12. Find the dimensions of a rectangular lawn knowing that the perimeter is 180 m long and one side

is 20 m longer than wider. 80 and 100

13. All sides of an equilateral triangle are x – 2 meters long.

a) Find an expression for the perimeter of the triangle. 3x - 6

b) If the perimeter is 12 meters long, calculate the value of x. 6

14. The base of a rectangle is x – 6 meters long, and its height is 4 meters. Find the value of x when

the area of the rectangle is 8 square meters. 8

15. A blouse has x buttons. A shirt has x + 2 buttons.

a) Write an expression for the number of buttons on four blouses. 4x

b) Write an expression for the number of buttons of three shirts. 3(x + 2)

c) Three shirts have the same number of buttons in total as four blouses. Write an equation

and solve it to find the value of x. 6

d) How many buttons are there on a shirt? 8


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16. Two cyclists leave the same point, at the same time in the same direction. The first one pedals at

a constant speed of 35 km/h and the second at 25 km/h. How long will it take them to be 15 km

apart? 1,5 hours

17. Two cars leave the same point at the same time, but in opposite directions. The first one is driven

at a constant speed of 85 km/h, and the second one at a constant speed of 90 km/h.

a) How many kilometers apart will they be in three hours? 525 km

b) How long will it take them to be 350 km apart? 2 hours

18. In a lake an electrical tower has been installed. One seventh of its height is under the ground at

the bottom of the lake, while 2/9 of the remaining stretch is immersed in the water. If the tower rises

14 meters above the lake surface, what is its total height? 21 meters

19. Jimmy bought two pens and a marker for a total of 5 euros. What was the price of each of the

items if a marker costs 0,5 euros more than a pen? Pen 1,5 eu and Marker 2 eu

20. A basket of apples weighs one kilo more than a basket of strawberries. Together, three baskets of

strawberries and two baskets of apples weigh 12 kg. How much does each box weigh? A 3kg S 2 kg

21. Calculate the value of a number if when you add 5 to the number and then multiply the result by

4, you get the same answer as when you add 1 to the number and then multiply the result by 2. -9

22. The length of a rectangle is twice the width. If the perimeter is 20 cm, find the width. 3,33 cm

23. The sum of four consecutive numbers is 90. Find the numbers. 21, 22, 23 and 24

24. Find three consecutive even numbers which add up to 1524. 506, 508 and 514

25. When a number is doubled and then added to 13, the result is 38. Find the number. 12,5

26. The sum of three numbers is 28. The second number is three times the first and the third is 7 less

than the second. What are the numbers? 7, 14 and 7

27. David weighs 5 kg less than John, who in turn is 8 kg lighter than Paul. If their total weight is

198 kg, how heavy is each person? D 60 J 65 P 73

28. The length of a rectangular lawn is 5 m longer than its width. If the area of the lawn is 176 square

meters, find the dimensions of the lawn. 11 and 16

29. Two positive numbers have a difference of 3 and their squares have a sum of 317. Let one of the

numbers be x. Write down an equation in x based on this information and solve it to find the two

numbers. x + = 317 11 and 14

30. The sides of a right-angled triangle are (2x + 1) and (3x + 2) long. If the area of this triangle is 13

square meters, calculate the value of x. 1,5

31. Two positive numbers which differ 3, have a product of 88. Find them. 8 and 11

32. The product of two positive and consecutive odd numbers is 143. Find the numbers. 11 and 13

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Unit 5 - Linear equations exercises and word problems 11/12