# How to find Q

#### jayomcd

##### New member
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
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
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

##### Senior Member
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

##### New member
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
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
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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