SOLUTION: Owen and Liam have some gold notebooks and some silver notebooks. The number of silver notebooks Owen has is equal to the number of gold notebooks Liam has. 3/4 of Owen's notebooks

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Owen and Liam have some gold notebooks and some silver notebooks. The number of silver notebooks Owen has is equal to the number of gold notebooks Liam has. 3/4 of Owen's notebooks      Log On


   

Question 1201242: Owen and Liam have some gold notebooks and some silver notebooks. The number of silver notebooks Owen has is equal to the number of gold notebooks Liam has. 3/4 of Owen's notebooks are gold and 1/3 of Liam's notebooks are silver. There are a total of 96 gold notebooks. Find the total number of notebooks they have.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52786) About Me  (Show Source):
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Owen and Liam have some gold notebooks and some silver notebooks.
The number of silver notebooks Owen has is equal to the number of gold notebooks Liam has.
3/4 of Owen's notebooks are gold and 1/3 of Liam's notebooks are silver.
There are a total of 96 gold notebooks. Find the total number of notebooks they have.
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Let x be the number of silver   notebooks that Owen has
and      the number of gold     notebooks that Liam has  (the same number).


Make this table based on the given info.

             Gold    Silver

    Owen                x

    Liam       x       



Since 3/4 of the Owen's notebooks are gold, their number is 3x.  So, your table becomes

             Gold    Silver

    Owen      3x        x

    Liam       x       



Since 1/3 of Liam's notebooks are silver, their number is x/2.  So, your table becomes

             Gold    Silver

    Owen      3x        x

    Liam       x       x/2



You are given that the total number of gold notebooks is 96:  3x + x = 96,  or  4x = 96,  x = 96/4 = 24.


Hence, the total number of notebooks they have is  96 + x + x/2 = 96 + 24 + 12 = 132.


ANSWER.  The total number of notebooks they have is 132.

Solved.