SOLUTION: A cup of coffee contains 20 more milligrams of caffeine than a cup of tea. A cup of coffee also contains 85 more milligrams of caffeine than the average cola drink. If one cup of t

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Question 1167981: A cup of coffee contains 20 more milligrams of caffeine than a cup of tea. A cup of coffee also contains 85 more milligrams of caffeine than the average cola drink. If one cup of tea and four cola drinks contain the same amount of caffeine as one cup of coffee, how many milligrams of caffeine are there in one cup of coffee?
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A cup of coffee contains 20 more milligrams of caffeine than a cup of tea. A cup of coffee also contains 85 more milligrams of caffeine than the average cola drink. If one cup of tea and four cola drinks contain the same amount of caffeine as one cup of coffee, how many milligrams of caffeine are there in one cup of coffee?
:
let c = amt of caffeine in a cup of coffee
let t = amt in tea
let a = amt in cola
write an equation for each statement
"A cup of coffee contains 20 more milligrams of caffeine than a cup of tea."
c = t + 20
"A cup of coffee also contains 85 more milligrams of caffeine than the average cola drink."
c = a + 85
"If one cup of tea and four cola drinks contain the same amount of caffeine as one cup of coffee, how many milligrams of caffeine are there in one cup of coffee?"
c = t + 4a
replace c with t+20 from the 1st statement
t + 20 = t + 4a
subtract t from both sides
20 = 4a
a = 20/4
a = 5 mg in a cola
In the 2nd equation replace a with 5
c = 5 + 85
c = 90 mg of caffeine in a cup of coffee

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
A cup of coffee contains 20 more milligrams of caffeine than a cup of tea.
A cup of coffee also contains 85 more milligrams of caffeine than the average cola drink.
If one cup of tea and four cola drinks contain the same amount of caffeine as one cup of coffee,
how many milligrams of caffeine are there in one cup of coffee?
~~~~~~~~~~~ 


Let x = "how many milligrams of caffeine are there in one cup of coffee" 

            (i.e. the unknown under the problem's question).


Then a cup of tea contains (x-20) milligrams of caffeine, and

     a cup of the average cola drink contains (x-85) milligrams of caffeine.


Next, we can write this equation

    cup of tea   and   four cola drinks contain   the same  amount of caffeine as one cup of coffee

      (x-20)      +      4*(x-85)                    =                   x


Simplify and find x

      5x          -      20-4*85                     =                   x

      5x          -         x                        =               20 + 4*85

      4x                                             =                 360

       x                                             =                 360/4 = 90.


ANSWER.  One cup of coffee contains 90 mg of caffeine.

Solved.