# Thread: equation

1. ## equation

Can anyone please tell me the steps needed to solve this:

r = 0.5272 x (r + 282); r = 314.4

I know the answer, I do not know to arrive at it.

2. Originally Posted by wjt
Can anyone please tell me the steps needed to solve this:

r = 0.5272 x (r + 282); r = 314.4

I know the answer, I do not know to arrive at it.
$\displaystyle r = 0.5272r + 148.6704$

$\displaystyle 0.4728r = 148.6704$

$\displaystyle r = \frac{148.6704}{0.4728}$

$\displaystyle r = 314 (3s.f.)$

3. ## Milo and equation

Thanks for your reply. Unfortunately, I am still in the dark as I can not understand how you arrived at the numbers. I am a very elderly man, long past remembering math and I ask that you help me through the equation step by step. Thank you.

4. Originally Posted by wjt
Thanks for your reply. Unfortunately, I am still in the dark as I can not understand how you arrived at the numbers. I am a very elderly man, long past remembering math and I ask that you help me through the equation step by step. Thank you.
which part do you not understand?

5. Originally Posted by wjt
I can not understand how you arrived at the numbers.
To learn the steps for solving linear equations, try here.

6. ## Milo and equation

Where did the "148.6704" and 0.4728 come from? What does sf mean? what does \frac mean? Sorry to be a nuisance but step by step is the only way I an learn at my age.

7. Originally Posted by wjt
Where did the "148.6704" and 0.4728 come from? What does sf mean? what does \frac mean? Sorry to be a nuisance but step by step is the only way I an learn at my age.
$\displaystyle r = 0.5272 * (r + 282)$

ok we need to multiply out the bracket.
$\displaystyle 0.5272*r = 0.5272r$
$\displaystyle 0.5272*282 = 148.6704$

so we get

$\displaystyle 1r = (0.5272r + 148.6704)$

right? get it?

$\displaystyle 1r-0.5272r = 0.5272r - 0.5272r + 148.6704$

which give us 0.4728r on the left hand side and 0r on the right hand side.

$\displaystyle 0.4728r = 148.6704$

then we just need to divide 0.4728 to find r.

$\displaystyle \frac{\rlap{/////}0.4728r}{\rlap{//////}0.4728}=\frac{148.6704}{0.4728}$

that will leave us $\displaystyle r= \frac{148.6704}{0.4728}$

put that in your calculator or do the division by hand.

you get $\displaystyle r = 314.4.$

3s.f. means 3 significant figures.

Hope this helps.