direction please?

[Guest]

A sample which is 20% Pendium, 50% Gulium and 30%Virdium weighs 6.8 grams/cc.
A sample which is 60% Pendium, 20% Gulium and 20%Virdium weighs 7.8 grams/cc.
A sample which is 30% Pendium, 30% Gulium and 40%Virdium weighs 6.8 grams/cc.
What is the weight of pure Gulium, in gms/cc?

Is either 5 or 9 the answer. THis is what I got, but I don't think I am using the right formula. Can someone show me what formula to use?

 

[stapel]

Is either 5 or 9 the answer. THis is what I got, but I don't think I am using the right formula.

It is unlikely that two different values would be the answer.

Please reply with the formula you are using, and showing the steps you have used to obtain your answers. Thank you.

Eliz.

 

[soroban]

Hello, adam40g!

The correct answer is indeed 5 . . . how did you get it?

A sample which is 20% Pendium, 50% Gulium and 30%Virdium weighs 6.8 grams/cc.
A sample which is 60% Pendium, 20% Gulium and 20%Virdium weighs 7.8 grams/cc.
A sample which is 30% Pendium, 30% Gulium and 40%Virdium weighs 6.8 grams/cc.
What is the weight of pure Gulium, in gms/cc?

Let \(\displaystyle P\) = grams of pure Pendium.
Let \(\displaystyle G\) = grams of pure Gulium.
Let \(\displaystyle V\) = grams of pure Virdium.

Sample #1 contains: . \(\displaystyle 0.2P\,+\,0.5G\,+\,0.3V\:=\:6.8\)
Sample #2 contains: . \(\displaystyle 0.6P\,+\,0.2G\,+\,0.2V\:=\:7.8\)
Sample #3 contains: .\(\displaystyle 0.3P\,+\,0.3G\,+\,0.4V\:=\:6.8\)

Eliminate the decimals by multiplying through by 10.

Solve the system: .\(\displaystyle \begin{array}{ccc}2P\,+\,5G\,+\,3V\:=\:68\\ 6P\,+\,2G\,+\,2V\:=\:78 \\ 3P\,+\,3G\,+\,4V\:=\:68\end{array}\)

\(\displaystyle \text{(I got: }P = 9,\;G = 7,\;V = 5.)\)