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If I have 1/4 of all the marbles and you have 1/3 of all the marbles, and we have 35 marbles between us, how many marbles are there altogether? How many do I have? How many do you have?



Answer :

[tex]\frac{1}{4}+\frac{1}{3}=\frac {3}{12}+\frac{4}{12}=\frac{7}{12}\\\\we\ have\ \frac{7}{12}\ of\ all\ the\ marbles\\\\m-the\ number\ of\ all\ marbles\\\\\frac{7}{12}m=35\Rightarrow m=35\times\frac{12}{7}=5\times12=60\\\\\frac{1}{4}\times60=15\\\\\frac{1}{3}\times60=20\\\\Answer:\\There\ are\ 60\ altogether\ marbles.\ I\ have\ 15\ marbles\\and\ you\ have\ 20\ marbles.[/tex]

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