At the end of the 2000 baseball season, the New York Yankees and the Cincinnati Reds had won a total of 31 World Series. The Yankees had won 5.2 times as many World Series as the Reds. How many World Series did each team win?

Question

whpalmer4 · Answer

let Y be the number of series won by the Yankees, and R be the number won by the Reds.  The problem gives us two relationships:
Yankees and Reds together have won 31 World Series $$Y+R = 31$$Yankees won 5.2 times as many as the Reds
$$Y=5.2R$$
Combine those two equations and solve for the values of Y and R.  Notice that the second equation conveniently gives you Y in terms of R with no work required, so you can just replace Y with 5.2R wherever you see it in the first equation.  That gives you an equation only in terms of R.  Solve that to find the number of series the Reds won.  Use the result to find how many series the Yankees won.

anonymous · Answer

I DO NOT GET IT

whpalmer4 · Answer

Do you see how I got those equations?

whpalmer4 · Answer

to solve, we do the substitution or replacement as I suggested:
Take the first equation$$Y+R=31$$and replace Y with the expression for Y from the second equation:$$5.2R + R = 31$$Can you solve that equation for R?

anonymous · Answer

no

whpalmer4 · Answer

collect like terms:
$$5.2R + R = 31$$$$6.2R = 31$$How about now?

anonymous · Answer

31=w+5.2w
 31=1w+5.2w
 31=6.2w
 ÷6.2w
 5=w
5 for w to get 26 for yankee and 5 for red

whpalmer4 · Answer

that's right!