Solve for p: 3q= 5/6s(3z/t+5m/p)

Question

campbell_st · Answer

so is the problem 

$$3q = \frac{5}{6s}(\frac{3z}{t} + \frac{5m}{p})$$

anonymous · Answer

Yes

anonymous · Answer

The first step is distributive property but everything is confusing after

agent0smith · Answer

Don't use distributive property first.

anonymous · Answer

Okay thanks

So what's first?

campbell_st · Answer

ok... this is a long question.... 

mutliply both sides of the equation by 6s

so 

$$18qs = 5(\frac{3z}{t} + \frac{5m}{p})$$

now divide both sides by 5

$$\frac{18qs}{5} = \frac{3z}{t} + \frac{5m}{p}$$

subtract 3z/t from both sides of the equation

$$\frac{18qs}{5} - \frac{3z}{t} = \frac{5m}{p}$$

hope this makes sense so far

anonymous · Answer

1 sec pls

campbell_st · Answer

the next step I'd recommend is put everything on the left hand side over a common denominator... just makes it easier...

anonymous · Answer

Then cancel out?

campbell_st · Answer

well start with the common denominator 

it will be 5t

$$\frac{18qs}{5} \times \frac{t}{t} - \frac{3z}{t} \times \frac{5}{5} = \frac{5m}{p}$$

so you get 

$$\frac{18 qst - 15z}{5t} = \frac{5m}{p}$$

does that make sense..?

anonymous · Answer

Where does t/t come from?

campbell_st · Answer

well its equal to 1... and you are using it to get the common denominator of 5t

campbell_st · Answer

happy to go on..?

anonymous · Answer

Yes..

anonymous · Answer

Ok I see

campbell_st · Answer

ok... here is a short cut... take the reciprocal of both fractions... 

$$\frac{5t}{(18qst - 15z)} = \frac{p}{5m}$$

does that make sense...?

anonymous · Answer

Yeah

anonymous · Answer

It can't be reduced?

campbell_st · Answer

last step... multiply both sides of the equation by 5m 

$$\frac{5t \times 5m}{(18qst - 15z)} = p$$

I'll let you finish it off... 

please go back and check the steps.

anonymous · Answer

Can 5t be cancelled out?

anonymous · Answer

25mt

campbell_st · Answer

nope... because 5t needs to be a factor of both terms in the denominator 

the only common factor in the denominator is 3

the 2nd part of the denominator, 15z,  doesn't comtain a t

and 18qst doesn't have 5 as a factor...

campbell_st · Answer

so the final answer is 

$$p = \frac{25mt}{(18qst - 15z)}$$

anonymous · Answer

I just found the answer
Distributive property would've been easier then multiplied the COmmon demon. by 3q
18pstq=15pz+25mt
P=25mt/18stq-15z

anonymous · Answer

Same answer but shorter

campbell_st · Answer

well its the same answer... and if you know fractions then the 1st step could have been 

divide both sides by 5/6s.... which is the same as multiplying by the reciprocal...

anonymous · Answer

Either way, wouldn't it be easier using distribute property?

anonymous · Answer

Shorter and simple

campbell_st · Answer

hope it all makes sense... good luck

agent0smith · Answer

ehhh... distributive property seems like more work, since you first have to distribute the 5/6s... it's already factored out, and distributing is undoing the work that was done to factor it out in the first place.

anonymous · Answer

I appreciate both of your help but i understand it so much better when I distribute 
Although I never understood the problem until it was explained, thank you

agent0smith · Answer

Fair enough, you can do it whichever way you prefer, distributing is still a valid way to re-arrange it.