Problems of linear and quadratic equations

Linear and quadratic equations

Mathematics

LINEAR AND QUADRATIC EQUATIONS PROBLEMS

PROBLEM 1 68 less than 5 times a number is equal to the number. Find the number.

PROBLEM 2 When 142 is added to a number, the result is 64 more than 3 times the number.

Find the number.

PROBLEM 3 Calvin Butterball buys a book for 14.70 â‚Ź, which is a price. What is the regular price of the book?

discount off the regular

PROBLEM 4 Two planes, which are 2400 miles apart, fly toward each other. Their speeds differ by 60 miles per hour. They pass each other after 5 hours. Find their speeds. (speed x time = distance) PROBLEM 5 Anne spends 2 hours training for an upcoming race. She runs full speed at 8 miles per hour for the race distance; then she walks back to her starting point at 2 miles per hour. How long does she spend walking? How long does she spend running?

Solution: Let x be the time she spent running. Since she spent 2 hours all together, she must have spent 2 - x hours walking.

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Linear and quadratic equations

Mathematics

Since she ran out, then turned around and walked back, her running and walking distances must be equal.

Set the distances equal and solve for x:

She spends 0.4 hours running and 2 - 0.4 = 1.6 hours walking.

PROBLEM 6 A train leaves the city at 2 p.m. A second train leaves the city at 8 p.m. and follows the first train. The second train's speed is 162 Km/h faster than the first train's. If the second train overtakes the first train at 10 p.m., what are the speeds of the two trains?

PROBLEM 7 1400â‚Ź is divided between two accounts. One account pays 3% interest, while the other pays 4% interest. At the end of one interest period, the interest earned was 50â‚Ź.

How much was invested in each account?

PROBLEM 8 The product of two consecutive integers is 56. Find the integers.

PROBLEM 9 The product of two consecutive integers is three less than three times their sum.

Find the integers.

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Linear and quadratic equations

Mathematics

PROBLEM 10 The product of two consecutive odd integers is 1 less than four times their sum.

Find the two integers.

PROBLEM 11 The length of a rectangle is 6 cm more than its width. The area of the rectangle is 91 square centimetres. Find the dimensions of the rectangle.

PROBLEM 12 The hypotenuse of a right-angled triangle is 6 cm more than the shorter side. The longer side is three cm more than the shorter side. Find the length of the shorter side.

PROBLEM 13 A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15m. Find the distance from the wall to the bottom of the ladder if the length of the ladder is one m more than twice its distance from the wall.

PROBLEM 14 Two cars leave an intersection. One car travels north; the other travels east. When the car traveling north had gone 24 km, the distance between the cars was four km more than three times the distance traveled by the car heading east. Find the distance between the cars at that time.

PROBLEM 15 During practice, a softball pitcher throws a ball whose height can be modeled by the equation h = -16t 2 + 24t +1, where h = height in metres and t = time in seconds. How long does it take for the ball to reach a height of 6 m?

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