Question 678412
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 {{{10000/(5-x)}}} and "the smallest number of bags" translates into {{{10000/(5+x)}}}. 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:
{{{10000/(5-x) = 100*(10000/(5+x))}}}<br>
Now we solve. I suggest we start by dividing both sides by 10000:
{{{1/(5-x) = 100*(1/(5+x))}}}
which simplifies to:
{{{1/(5-x) = 100/(5+x)}}}
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):
{{{(5-x)(5+x)(1/(5-x)) = (5-x)(5+x)(100/(5+x))}}}
The denominators cancel:
{{{cross((5-x))(5+x)(1/cross((5-x))) = (5-x)cross((5+x))(100/cross((5+x)))}}}
leaving:
{{{(5+x)(1) = (5-x)(100)}}}
which simplifies to:
{{{5+x = 500-100x}}}
Adding 100x:
{{{5+101x = 500}}}
Subtracting 5:
{{{101x = 495}}}
Dividing by 101:
{{{x = 495/101}}}<br>
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.