Help with Mathematics Please?????????????

Question

$M is just sufficient to pay the wages of one clerk for x days or the wages of one secretary for y days.
Express the maximum number of days $M can be used to pay the combined wages of one clerk and one secretary in terms of x and y.

Answer 1

$M = clerk salary for x days = CS * x
$M = secretary salary for y days = SS * y

CS * x = $M = SS * y

What you want to do is pay both of them for "d" days, so that:

$M = CS * d + SS * d = (CS + SS) * d, or

d = $M/(CS + SS)

and we want to express d as a function of x and y:

Now, since CS * x = SS * y, we can rearrange to:

CS = SS * y/x

Let's substitute that into the equation above to get:

d = $M/(CS + SS) = $M/({SS * y/x} + SS)

simplifying to:

d = $M/{SS(y/x + 1)}

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Another approach is as follows:

M = CS * x = SS * y, thus:

CS = M/x and SS = M/y

If we want to pay both for a number of days d, then:

M = (CS * d) + (SS * d) = (d * M/x) + (d * M/y)

M = (dMy + dMx)/xy

1 = d * (y + x)/xy

d = xy/(x+y)

Depends on just how much information you have. If you know salaries (CS and SS), then you can use my first equation.

If you only know the numbers of days (x + y), then the second answer is best. Either way, you come up with the same answer.

Answer 2

I came up with the same answer x*y/(x+y), was a bit puzzled that the M fell out of the equation (but it is correct seeing that x and y change as M changes and the salaries stay the same). I dont see the leap to M/2 though... x*y/(x+y) is your answer for total days both can be paid!

And as for Dave's answer, yes if I would know SS and CS I wouldnt need to express it in x and y now would I? Introducing the variables is good, but you can't leave them in the answer.. or am I wrong?

Answer 3

Yeesh. Sort of confusing. The problem is to find the maximum number of days M will pay both. Well, this means you need to find the cost per day of both, then add them, then divide M by that number.

Cost per day of the clerk: M=cx--> 1day costs M/(cx)
Cost per day of secretary: M=sy--> 1day costs M/(sy)

Cost of secretary and clerk for 1 day--> M/(cx)+M/(sy)

Number of days available-->M/[M/(cx)+M/(sy)]

This simplifies to (cx)(sy)/(cx+sy).

But Cx=M and sy=M, so that this becomes M^2/(2M)=M/2.
So the answer is M/2 days.

Answer 4

Maybe this will help you.

$M = x times c
$M = y times s

C being clerk, s being secretary

So... $M = (x times c + y times s)/2

Answer 5

same notation as above:

1M = c*x

1M = s*y

and 1M/(c+s)=result

then:

1M/(1M/x+1M/y)=result

which simplifies to result=x*y/(x+y)

Answer 6

G = K + m&m's......yummy