Wordproblem
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The document contains 25 word problems involving quadratic equations. The problems cover a range of topics including finding unknown numbers given information about sums and differences of squares, finding dimensions of rectangles and triangles, modeling population growth and projectile motion, and maximizing revenue. Students are asked to solve for unknown values or find answers that satisfy given conditions in each problem.
Wordproblem
- 2. 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 = 9 times the number = T.Yodhathai reesrikom
- 3. Your work1. 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 = 8 times the number = AnswerT.Yodhathai reesrikom
- 4. 2. A certain number added to its square is 30. Find the number.A certain number = its square = T.Yodhathai reesrikom
- 5. Your work2. A certain number added to its square is 56. Find the number.A certain number = its square = T.Yodhathai reesrikom
- 6. 3. The square of a number exceeds the number by 72. Find the number.a number = square of a number = T.Yodhathai reesrikom
- 7. 4. Find two positive numbers whose ratio is 2:3 and whose product is 600.First numbers =numbers whose ratio is 2:3 = 2x:3xproduct is 600 =T.Yodhathai reesrikom
- 8. positive numbers two positive numbers T.Yodhathaireesrikom
- 9. 5. The product of two consecutive odd integers is 99. Find the integers.odd integers =consecutive odd integers = If x = 9 consecutive odd integers= 9+2=11If x = -11 consecutive odd integers= -11+2=-9T.Yodhathaireesrikom
- 10. 6. Find two consecutive positive integers such that the square of the first is decreased by 17 equals 4 times the second.First number = Second number = First number = 7 Second number = 7+1=8T.Yodhathaireesrikom
- 11. 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 =oldest child =T.YodhathaireesrikomThe ages of three family children = 10,11,12 year old
- 12. 8. Find three consecutive odd integers such that the square of the first increased the product of the other two is 224.three consecutive odd integers = 9,10,11 T.Yodhathaireesrikom
- 13. 9. The sum of the squares of two consecutive integers is 113. Find the integers.If x= 7 two consecutive integers is 7 and 8 If x= -8 two consecutive integers is -8 and -7T.Yodhathaireesrikom
- 14. 10. The sum of the squares of three consecutive integers is 302. Find the integers.If x= -11 three consecutive integers is -11,-10,-9If x= 9 three consecutive integers is 9,10,11T.Yodhathaireesrikom
- 15. 11. Two integers differ by 8 and the sum of their squares is 130.If integers is -3 two integers is -3 and -11If integers is 11 two integers is 11 and 3T.Yodhathaireesrikom
- 16. 12. rectangle is 4 m longer than it is wide, its area is 192 m2. Find the dimensions of the rectangle.Dimensions of the rectangle= 12 x 16 = 192 T.Yodhathaireesrikom
- 17. 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.the dimensions is 6 and 8 T.Yodhathaireesrikom
- 18. 14. The sum of the squares of three consecutive even integers is 980. Determine the integersIf x = 16 three consecutive even integers is 16,18,20 If x = -20 three consecutive even integers is -20,-18,-16 T.Yodhathaireesrikom
- 19. 15. Two integers differ by 4. Find the integers if the sum of their squares is 250. ( same No.11)If integers is 13 two integers is 13 and 9If integers is -9 two integers is -9 and -13T.Yodhathaireesrikom
- 20. 16. Find three consecutive integers such that the product of the first and the last is one less than five times the middle integer.If x = -1 three consecutive integers = -1,0,1 If x = 4 three consecutive integers = 4,5,6 T.Yodhathaireesrikom
- 21. 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?T.Yodhathaireesrikom
- 22. 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?The dimensions of the field= 9x12=108T.Yodhathaireesrikom
- 23. 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.T.Yodhathaireesrikom
- 25. 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.
- 27. 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.
- 28. The width of the margin= 10+7 = 17
- 29. 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
- 31. 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?George need to sell to break even =20+7 = 27
- 32. 24.A biologist predicts that the deer population, P, in a certain national park can be modelled by 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
- 33. b) Will the deer population ever reach zero?No answerNo chance that the population of deer will be 0.
- 34. c) In what year will the population reach 1000?18 year will the population reach 1000
- 35. 25.A t-ball player hits a baseball from a tee. The flight of the ball can be modelled by 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?
- 36. b) How long does it take the ball to land?the ball take to land
- 38. c) When does the ball reach a height of 4.5 m?
- 39. 1.1360.74.5