three chemical reactions produce different volumes with a combined total of 560cm^3, A produces double of B and C is double of A find each volume

Question

Three chemical reactions each produce oxygen. If the first produces twice that of the second, the third produces twice that of the first, and the combined total is 560cm^3, what volume is produced by each

Answer 1

There are three unknown quantities, so three equations are needed:

A + B + C = 560

 

A = 2B  --> B = A/2

 

C = 2A

 

 

Substituting the last two equations into the first gives:

 

  A +  B  + C = 560

 

  A + A/2 + 2A = 560  because B = A/2 per the second equation and C = 2A per the third equation

 

 Multiplying both sides by two to clear the fraction, the equation becomes:

 

 2A + A + 4A = 1120

 

 7A = 1120  <-- after combining like terms

 

 A = 160

 

 B = A/2 = 160/20 = 80

 

 C = 2A = 2*160 = 320

 

Finally, A + B + C = 160 + 80 +320 = 560