How to find Q

jayomcd

New member
Joined
Mar 9, 2019
Messages
3
Hello,

I'm struggling with this following equation:

90-0.8Q=30

My intention is to find the value of Q.

My initial reaction is to try to isolate Q by taking it over to 30 so the equation would be 90-0.8=30/Q

But I'm not sure where to go from here - can anyone help?

Thanks,
Jason
 

MarkFL

Super Moderator
Staff member
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Nov 24, 2012
Messages
994
I would first subtract 90 from both sides:

\(\displaystyle -0.8Q=-60\)

Now, multiply both sides by -1:

\(\displaystyle 0.8Q=60\)

Can you continue?
 

jayomcd

New member
Joined
Mar 9, 2019
Messages
3
Thanks for the help.

So I would now be inclined to reorder the equation as follows:

Q = 60/0.8
Q = 75

I think this makes sense because 90 - (0.8x75) = 30

Is that correct?

Thanks once again...
 

ksdhart2

Full Member
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Mar 25, 2016
Messages
962
My initial reaction is to try to isolate Q by taking it over to 30 so the equation would be 90-0.8=30/Q
The idea behind what you did is good, but the execution is flawed because you performed an "illegal" operation. You can't divide just one term in an expression - it's an all or nothing package deal. Consider the following:

\(\displaystyle 2x = 8\)

If we wanted to know the value of x, we could divide both sides by 2, yielding:

\(\displaystyle \frac{2x}{2} = \frac{8}{2} \implies x = 4\)

Now, consider a slight variant on that exercise:

\(\displaystyle 2x + 1 = 9\)

Let's proceed with the exact same type of operation you did in your post, and divide only the x term by 2:

\(\displaystyle \frac{2x}{2} + 1 = \frac{9}{2} \implies x + 1 = \frac{9}{2} \implies x = \frac{7}{2}\)

We can then plug this back in to check our answer:

\(\displaystyle 2 \left(\frac{7}{2} \right) + 1 = 7 + 1 = 8 \neq 9\)

Oh dear, that's not right at all! But where did we go wrong? Recall what I said earlier about division. What we should have done is:

\(\displaystyle \frac{2x + 1}{2} = \frac{9}{2} \implies x + \frac{1}{2} = \frac{9}{2} \implies x = \frac{8}{2} = 4\)

Ah, much better, that worked exactly as we intended.
 

jayomcd

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Joined
Mar 9, 2019
Messages
3
Ok - great. Thanks for the explanation.

So the next step in my equation is to divide both sides by 0.8?

0.8Q/0.8 = 30/0.8

Q = 37.5

That doesn't seem to work when I plug it into the equation so I think I've gone wrong somewhere again?

Thanks for the help...
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
994
Thanks for the help.

So I would now be inclined to reorder the equation as follows:

Q = 60/0.8
Q = 75

I think this makes sense because 90 - (0.8x75) = 30

Is that correct?

Thanks once again...
Yes, this is correct. :)
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
2,965
Hello,

I'm struggling with this following equation:

90-0.8Q=30

My intention is to find the value of Q.

My initial reaction is to try to isolate Q by taking it over to 30 so the equation would be 90-0.8=30/Q

But I'm not sure where to go from here - can anyone help?

Thanks,
Jason
You need to think of this as a puzzle. 0.8Q is unknown, but you know that 90 minus this unknown number is 30. So you think, what 90 minus what number is 30. The answer is 60, that is 90-60 = 30. So 0.8Q = 60.
Now you need to know this type of pattern: If 2*5=10, then 10/2=5. That is if ab=c, then c/a=b. Know this like you know your own name! So from 0.8Q = 60 we get Q = 60/0.8.


That last step should take less than 1 second, seriously!

Consider these few examples and their immediate answers
3x=13, then 13/3 = x
22x=19, then 19/22 = x
.3x=77, then 77/.3 = x

No need at all to formally divide sides by the same thing. This pattern was taught to you in grade 4 but unfortunately many algebra teachers forgot that pattern.
 
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