This is hard...

[dancebear]

does anyone know the answer to...

In the summer olympics, the US,Russia, China, Aus., and Germany won a total of 359 medals. THe us won 19 fewer medals than twice the number of medals Aus. one. Russia won 28 fewer medals than twice the number of medals Aus. won. China won 1 more medal than Aus. won. Germany won 1 fewer medal than Aus. won. Determine the number of medals won by the US, Russia, China, Aus. and Germany in the 2000 summer olympics...

Thanks alot

 

[TchrWill]

We know that U + R + C + A + G = 359

We arwe also told that
U = 2A - 19
R = 2A - 28
C = A + 1
G = A -- 1

Substitute for U, R, C and G and you will be on your way to the anserws.

 

[soroban]

Hello, dancebear!

Did you try to write some equations?

In the summer olympics, the US, Russia, China, Aus., and Germany won a total of 359 medals.
\(\displaystyle \;\;\;\)[1] \(\displaystyle \;U\,+\,R\,+\,C\,+\,A\,+\,G\;=\;359\)

The US won 19 fewer medals than twice the number of medals Aus. won.
\(\displaystyle \;\;\)[2] \(\displaystyle \;U\;=\;2A\,-\,19\)

Russia won 28 fewer medals than twice the number of medals Aus. won.
\(\displaystyle \;\;\)[3] \(\displaystyle \;R\;=\;2A\,-\,28\)

China won 1 more medal than Aus. won.
\(\displaystyle \;\;\)[4] \(\displaystyle \;C\;=\;A\,+\,1\)

Germany won 1 fewer medal than Aus. won.
\(\displaystyle \;\;\)[5] \(\displaystyle \;G\;=\;A\,-\,1\)

Determine the number of medals won by each country.

Substitute [2], [3], [4], [5] into [1]:


\(\displaystyle \;\;\;\;\;\;U\;\;\;+\;\;\;R\;\;\;+\;\;\;C\;\;\;+\;A\;+\;\;G\;=\;359\)
. . . . . . \(\displaystyle \downarrow\;\;\;\;\;\;\;\;\downarrow\;\;\;\;\;\;\;\downarrow\;\;\;\;\;\;\downarrow\;\;\;\;\downarrow\)
\(\displaystyle \;\;(2A\,-\,19)\,+\,(2A\,-\,28)\,+\,(A\,+\,1)\,+\,A\,+\,(A\,-\,1) \;= \;359\)

And solve for \(\displaystyle A\) . . . etc.