Wordproblem

Word problem

ofQuadratic

T.YODHATHAI REESRIKOMwww.tsomath.com

1. When the square of a certain number is diminished by 9 times the number the result is 36. Find the number.

square of a certain number = 2x

9 times the number = x9

3692 xx

03692 xx0)3)(12( xx

312 orx


1. When the square of a certain number is diminished by 8 times the number the result is 9. Find the number.

square of a certain number = 2x

8 times the number = x8

982 xx

0982 xx0)1)(9( xx

19 orx

Your work

AnswerT.YODHATHAI REESRIKOMwww.tsomath.com

2. A certain number added to its square is 30. Find the number.

A certain number = xits square =

2x

302 xx

0302 xx0)5)(6( xx

5)6( orx


2. A certain number added to its square is 56. Find the number.

A certain number = xits square =

2x

562 xx

0562 xx0)7)(8( xx

7)8( orx

Your work


3. The square of a number exceeds the number by 72. Find the number.

a number = xsquare of a number =

2x

722 xx0722 xx0)8)(9( xx

89 orx


4. Find two positive numbers whose ratio is 2:3 and whose product is 600.

numbers whose ratio is 2:3 = 2x:3xFirst numbers = x

xx2

3:

product is 600 = 600)2

3( xx

6002

3 2

x

12003 2 x

3

12002 x

4002 x

04002 x

02022 x


0)20)(20( xx

2020 orx

20xpositive numbers

two positive numbers 30:20)20(2

3:20

2

3: xx


5. The product of two consecutive odd integers is 99. Find the integers.

odd integers = xconsecutive odd integers = 2x

99)2( xx9922 xx09922 xx0)11)(9( xx

119 orx

If x = 9 consecutive odd integers= 9+2=11

If x = -11 consecutive odd integers= -11+2=-9


6. Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the second.

First number = xSecond number = 1x

)1(4172 xx0)1(4172 xx044172 xx02142 xx0)3)(7( xx

37 orx7x

First number = 7 Second number = 7+1=8


7. The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than eight times the age of the oldest child. Find the ages of the three children.

youngest child = xoldest child = 2x

)2(842 xx16842 xx

02082 xx0)10)(2( xx

102orx 10x

The ages of three family children = 10,11,12 year oldT.YODHATHAI REESRIKOM

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8. Find three consecutive odd integers such that the square of the first increased the product of the other two is 224.

224)4)(2(2 xxx2248622 xxx021662 2 xx010832 xx0)9)(12( xx

912orx 9x

three consecutive odd integers = 9,10,11


9. The sum of the squares of two consecutive integers is 113. Find the integers.

113)1( 22 xx1131222 xxx011222 2 xx0562 xx0)8)(7( xx

87 orx

If x= 7 two consecutive integers is 7 and 8 If x= -8 two consecutive integers is -8 and -7


10. The sum of the squares of three consecutive integers is 302. Find the integers.

302)2()1( 222 xxx302)44()12( 222 xxxxx

029763 2 xx09922 xx0)9)(11( xx

911orx

If x= -11 three consecutive integers is -11,-10,-9If x= 9 three consecutive integers is 9,10,11


11. Two integers differ by 8 and the sum of their squares is 130.

130)8( 22 xx130641622 xxx066162 2 xx03382 xx0)11)(3( xx

113 orx If integers is -3 two integers is -3 and -11If integers is 11 two integers is 11 and 3


12. rectangle is 4 m longer than it is wide, its area is 192 m2. Find the dimensions of the rectangle.

192)4( xx19242 xx019242 xx0)12)(16( xx

1216 orx 12x

12

412

Dimensions of the rectangle= 12 x 16 = 192


13. right triangle has a hypotenuse of 10 m. If one of the sides is 2 m longer than the other, find the dimensions of the triangle.

222 bac 222 )2(10 xx4410 222 xxx100440 22 xxx

96420 2 xx)8)(6(0 xx

86 orx

6x

the dimensions is 6 and 8


14. The sum of the squares of three consecutive even integers is 980. Determine the integers

222 )4()2(980 xxx

)168()44(980 222 xxxxx20123980 2 xx

980201230 2 xx

32040 2 xx)20)(16(0 xx

2016 orx

If x = 16 three consecutive even integers is 16,18,20

If x = -20 three consecutive even integers is -20,-18,-16


15. Two integers differ by 4. Find the integers if the sum of their squares is 250. ( same No.11)

250)4( 22 xx25016822 xxx023482 2 xx011742 xx0)9)(13( xx

913 orx

If integers is 13 two integers is 13 and 9If integers is -9 two integers is -9 and -13


16. Find three consecutive integers such that the product of the first and the last is one less than five times the middle integer.

)1(51)2( xxx55122 xxx

055122 xxx0432 xx0)4)(1( xx

41 orx If x = -1 three consecutive integers = -1,0,1 If x = 4 three consecutive integers = 4,5,6


17. A rectangle is three times as long as it is wide. Its area has measure equal to ten times its width measure plus twenty-five. What is the width?

2510)3( xxx025103 2 xx0)5)(53( xx

53

5orx

5x


18. Richie walked 15 m diagonally across a rectangular field. He then returned to his starting position along the outside of the field. The total distance he walked was 36 m. What are the dimensions of the field?

222 )21(15 xx 2242441225 xxx

2164220 2 xx108210 2 xx)12)(9(0 xx

129orx

The dimensions of the field= 9x12=108


19. A square picture with sides of length 20 cm is to be mounted centrally upon a square frame. If the area of the border of the frame equals the area of the picture, find the width of the border of the frame to the nearest millimetre.

)20(4202 xx 220

4

400xx 220100 xx

0100202 xx

a

acbbx

2

42


85108510 orx142.24142.4 orx

142.4x

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20. A square lawn is surrounded by a walk 1 m wide. The area of the lawn is equal to the area of the walk. Find the length of the side of the lawn to the nearest tenth of a metre.

)1(42 xx442 xx

0442 xx

a

acbbx

2

42

12

)4(14)4()4( 2

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222222 orx

828.0828.4 orx

828.4x

5x

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21. A picture 20 cm wide and 10 cm high is to be centrally mounted on a rectangular frame with total area three times the area of the picture. Assuming equal margins for all four sides, find the width of the margin.

10203102202 xxxx

0600604 2 xx

0150152 xx

2

3315

2

3315 orx

861.2861.6 orx

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7861.6 xThe width of the margin= 10+7 = 17

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22. A fast food restaurant determines that each 10¢ increase in the price of a hamburger results in 25 fewer hamburgers sold. The usual price for a hamburger is $2.00 and the restaurant sells an average of 300 hamburgers each day. What price will produce revenue of $637.50?

100¢ = $1 10¢ = $ 0.1

5.6371.025

)300()300(2

xx

5.637)25

1.02)(300( x

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5.637)996.1)(300( x

996.1

5.637)300( x

38.319300 x

30038.319 x

38.19x

20x

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23. George operates his own store, George’s Fashion. A popular style of pants sells for $50. At that price, George sells about 20 pairs of pants a week. Experience has taught George that for every $1 increase in price, he will sell one less pair of pants per week. In order to break even, George needs to produce $650/week. How many pairs of pants does George need to sell to break even?

650)20(50 xx506501000

750

350x

George need to sell to break even =20+7 = 27www.tsomath.com

24.A biologist predicts that the deer population, P, in a certain national park can be modelled by 28 112 570,P x x

where x is the number of years since 1999.a) According to the model, how many deer were in the park in 1999.b) Will the deer population ever reach zero?c) In what year will the population reach 1000?

a) According to the model, how many deer were in the park in 1999 1x

570)1(112)1(8 2 p466p

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b) Will the deer population ever reach zero?

0p

57011280 2 xx

No answerNo chance that the population

of deer will be 0.

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c) In what year will the population reach 1000?

57011281000 2 xx43011280 2 xx

a

acbbx

2

42

2

41114x

137.3137.17 orx 137.17x18x

18 year will the population reach 1000

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25. A t-ball player hits a baseball from a tee. The flight of the ball can be modelled by

24.9 9 0.6h t t where h is the height in metres, and t is the time in seconds.a) How high is the tee?b) How long does it take the ball to land?c) When does the ball reach a height of 4.5 m?

a) How high is the tee? 0t

6.0

6.0)0(9)0(9.4

6.099.42

2

h

h

tth

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b) How long does it take the ball to land?

the ball take to land 0h6.099.4 2 tth

6.099.40 2 tt6.099.40 2 tt690490 2 tt

a

acbbt

2

42

)49(2

)6)(49(4)90()90( 2 t

)49(2

1176810090 t

)49(

23145t

064.09.1 ort

9.1t

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c) When does the ball reach a height of 4.5 m?

5.4h

6.099.45.4 2 tt5.46.099.40 2 tt

9.399.40 2 tt9.399.40 2 tt3990490 2 tt

a

acbbt

2

42

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a

acbbt

2

42

49

11445t

7.0136.1 ort

4.5

0.7 1.136

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