EXOEXOEXO
  • EXOEXOEXO
every marble in a jar has either a dot, a stripe, or both. the ratio of striped marbles to non striped marbles is 3:1, and the ratio of dotted marbles to non dotted marbles is 2:3. if six marbles have both a dot and a stripe, how many marbles are there all together?
Mathematics
schrodinger
  • schrodinger
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mathmate
  • mathmate
Let s=number of striped marbles (includes both striped and dotted) d=number of dotted marbles (includes both striped and dotted) 6=number of both then d-6=number of non-striped marbles s-6=number of non-dotted marbles We have s/(d-6)=3/1 => s=3(d-6) ...(1) d/(s-6)=2/3 => 3d=2(s-6) ...(2) solve for s and d To check your answer, number of striped is slightly less than twice the dotted ones, or put back you solutions into (1) and (2) and see if the equations hold.
anonymous
  • anonymous
Let the number of marbles with a dot be \(x\) and the number of marbles with a stripe be \(y\). Then the number of non-dotted marbles is y+6 and the number of non-striped marbles is x+6. Employing the given ratios we have\[3(y+6)=x\]\[2(x+6)=3y\]Solve this system for \(x\) and \(y\), and add 6 to the total.
anonymous
  • anonymous
Messed my system of equations up

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anonymous
  • anonymous
\[y+6=3x\]\[3(x+6)=2y\]That's better

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