SOLUTION: There are 10 tonnes of potatoes in a large container. Bags of potatoes of nominal mass 5kg are filled from this container. the potatoes are not all the same size and it is not po

Click here to see ALL problems on Quadratic Equations

Question 678412: There are 10 tonnes of potatoes in a large container. Bags of potatoes of nominal mass 5kg are filled from this container.
the potatoes are not all the same size and it is not possible to make the bags exactly 5kg. (1 tonne = 1000kg)
1) If all the bags could be made with a mass of exactly 5kg. How many bags would be filled from the container?
My answer: 10000 / 5 = 2000
The bags could be light by up to xkg or too heavy by up to xkg
2) State , in terms of x, the largest and smallest number of bags that can be filled from the container
My answer: Largest number 10000 / (5 - x), Smallest number 10000 / (5 + x)
3) Given that the largest number of bags is 100 times more than the smallest number of bags, write down an equation in x and show that it simplifies to x2 ( x squared) + 200x - 25 = 0
My answer: ??? Can't remember how to do these
4) Solve this equation and hence work out the largest and smallest mass of a bag of potatoes.
My answer: and therefore this
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
You;ve done very well up to part 3. To do part 3 you just translate "the largest number of bags is 100 times more than the smallest number of bags" into an equation. You have already found that "the largest number of bags" translated into and "the smallest number of bags" translates into . And since "is" translates into "=" and "100 times more" translates into "100*", "the largest number of bags is 100 times more than the smallest number of bags" translates into:

Now we solve. I suggest we start by dividing both sides by 10000:

which simplifies to:

Now let's eliminate the fractions. We can do this by finding the least common denominator (LCD) of the fractions (on both sides). The LCD here is simply the product of the two denominators. So we multiply both sides by (5-x)(5+x):

The denominators cancel:

leaving:

which simplifies to:

Adding 100x:

Subtracting 5:

Dividing by 101:

The largest mass bag is 5+x and the smallest mass bag is 5-x. I'll leave it up to you to find these using the above value for x.