Could someone help me rearrange this equation

I'm doing some chemistry revision, and I can't seem to get past this one bit...My mind blanking.

(27.8)-t15.2=(492.7)-t542

I need to figure out the value of t, and I can't seem to do it.

I checked the mark scheme for the answer, and the bit I have it right. It just doesn't give an explanation of how you rearrange for t.

Any help would be appreciated!

(p.s. I tried wolfram alpha, it didn't give me the rearranged formula; but if I remember correctly the values is 0.9 something!)

Add 542 t to both sides to obtain

27.8 + 542 t - 15.2 t = 492.7
which when grouping the terms with t gives
27.8 + 526.8 t = 492.7

Then subtract 27.8 from both sides to obtain

526.8 t = 464.9

finally divide both sides by 526.8 and end up with

t = 464.9 / 526.8 = 0.882

27.8 - t15.2 = 492.7 - t542 ....< Rearrange so that all the numbers & 't's are grouped on separate sides

27.8 - 492.7 = - t542 + t15.2

27.8 - 492.7 = t( - 542 + 15.2 ) ....< remove the common term 't' from the RHS

- 464.9 = t (- 526.8) .... < simplify and divide both sides by -526.8

t = - 464.9 / - 526.8

t = 0.8824981017 or 4649/5268 as the smallest integer fraction

I don't know chemistry well but I do know algebra. This is how I would go about your problem.

(27.8) - t15.2 = (492.7) - t542 move t to the left side and constants to the right
526.8t = 464.9 divide the constant by the factor of t
t = 0.88

Hope this helps

(27.8)-t15.2=(492.7)-t542
or 27.8-15.2t=492.7-542t
or 542t-15.2t=492.7-27.8
or 526.8t=464.9
or t=464.9/526.8
or t=0.8825

27.8 - 15.2t = 492.7 - 542t

=> 542t - 15.2t = 492.7 - 27.8

=> 526.8t = 464.9

i.e. t = 464.9/526.8 = 0.88 (2 d.p.)

:)>

542t-15.2t=492.7-27.8