Sauder has three times as much money as Sony. Sammy has $4 less than Sauder and $5 more than Sony. How much money does each have?

1 Answer
KillerBunny
Oct 14, 2015

Sauder has #13.5#$, Sony has #4.5#$, Sammy has #9.5#$.

Explanation:

Why they all have names with the same letters! :P Anyway, let's call Sauder #a#, Sony #b# and Sammy #c#. Translating into equation, we have

  • Sauder has three times as much money as Sony #-> a=3b#;
  • Sammy has $4 less than Sauder #-> c=a-4#;
  • Sammy has $5 more than Sony #-> c=b+5#

And let's solve the system. Given the first equation, we can substitute #a# with #3b#. By doing so, second and third equations become

#c=3b-4#
#c=b+5#

Since both #3b-4# and #b+5# equal to #c#, they must be equal to each other, so we have #3b-4=b+5#, and solving for #b# we get #2b=9#, and thus #b=9/2=4.5#.

Now that we know #b#, we can easily find #a# and #c#:

#a=3b=3*4.5=13.5#
#c=a-4=b+5=13.5-4=4.5+5=9.5#

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