SOLUTION: Ben has some marbles. 4/7 of the marbles are red and the rest are blue. If he has 18 blue marbles, how many marbles does Ben have altogether ?

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Question 1144740: Ben has some marbles. 4/7 of the marbles are red and the rest are blue. If he has 18 blue marbles, how many marbles does Ben have altogether ?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

From the condition,  3%2F7  marbles are blue.


Hence,  3%2F7 of the marbles are 18 blue marbles.


It means, that  1%2F7 of the marbles is  18%2F3 = 6 marbles.


Therefore, the number of the blue marbles is 6*7 = 42.


Altogether, Ben has 18 + 42 = 60 marbles.    ANSWER


Solved MENTALLY, without using equations.



Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Ben has some marbles. 4/7 of the marbles are red and the rest are blue. If he has 18 blue marbles, how many marbles does Ben have altogether ? 
With 4%2F7 being red, matrix%281%2C3%2C+1+-+4%2F7%2C+or%2C+3%2F7%29 is blue.

We then get the following PROPORTION, with T being the total number of marbles: matrix%281%2C3%2C+%283%2F7%29%2F1%2C+%22=%22%2C+18%2FT%29     

matrix%281%2C3%2C+3T%2F7%2C+%22=%22%2C+18%29 ------ Cross-multiplying

3T = 7(18) ----- Cross-multiplying

T, or total number of marbles =