SOLUTION: Hi Bob had twice as many books as Tom. Carl had 5 times as many books as Tom. When Bob received some books and Tom bought another 180 books they all had the same number of books.

Question 1195203: Hi
Bob had twice as many books as Tom. Carl had 5 times as many books as Tom. When Bob received some books and Tom bought another 180 books they all had the same number of books.
How many did they have altogether.
Thanks
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let B equal the number of books that bob had.
let T equal the number of books that tom had.
let C = the number of books that carl had.

your equations are:
B = 2T
C = 5T
B + x = T + 180 = C
this equations says that they're all equal after adding x books to B and 180 books to T.
replace B with 2T and C with 5T to get:
2T + x = T + 180 = 5T
break this up into two separate equalities to get:
2T + x = T + 180
T + 180 = 5T
in the second equation, solve for T to get:
T = 45
using that value of T, solve for x in the equation to get:
2T + x = T + 180 becomes:
90 + x = 45 + 180 which becomes:
90 + x = 225 which becomes:
x = 135.
since x = 135 and T = 45, go back to your original equations to see if they're true.
you get:
B = 2T becomes B = 90
C = 5T becomes C = 225
B + x = T + 180 = C becomes 90 + 135 = 45 + 180 = 225 which becomes:
225 = 225 = 225
this confirms the solution is correct.
the solution is that they had 3 * 225 = 675 books all together.

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