Quandaries and Queries


Who is asking: Student
Level: Middle

i think i know the basics of how to solve direct quadratic equations,but how do i go about solving those word problems? i have tried them times and again, but nothing seems to work at all!they are driving me crazy! pls help!:):):):):)

  1. bob & nick earned $1260 each. bob's hourly wage is $3 more than nick's hourly wage. he worked 2h less compared to nick. find the number of hours nick worked.
  2. there are 2 tanks in henry's house. in tank A, the fish are all goldfish. they are bought at a total cost of $259. in tank B, there are only guppies. the guppies were bought at a cost of $1.20 each. a day later,henry bought 3 more goldfish and put them into tank A. the number of guppies in tank B is now twice the number of goldfish in tank A.the total cost of all the fish that henry has presently,i.e. goldfish & guppies, is $355.30. given that the cost of each goldfish is the same,
    a)find the initial number of goldfish in tank A
    b)find the total cost of all the guppies.
  3. a particular disc can be made to rotate at 2 different speeds. if it is made to rotate slower by 135 revolutions per hour, it wld require an additional 2.7 hour to make 315 revolutions. find the higher speed at which it can operate.



For problem 1 the amount each man earned is his hourly rate times the number of hours he worked. Lets start with Bob. Suppose that Bob makes $R per hour and he worked for H hours. We know that he earned $1260 so

RH = 1260

Now Nick. Bob's hourly rate is $3 more than Nick's so Nick's hourly rate is $(R-3).Bob worked 2 hours less than Nick so Nick worked H+2 hours. We know that Nick earned $1260 also so,

(R-3)(H+2) = 1260

From the first equation, R = 1260/H and hence, substituting into the second equation we get.

1260/H -3)(H+2) = 1260

I would now multiply each side of the equation by H to get

(1260 -3H)(H+2) = 1260H

which simplifies to

H2 +2H -840 = 0

Solve the quadratic equation for H and then, finally, Nick worked H+2 hours.




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