SOLUTION: In one day, Machine A caps twice as many bottles as machine B {{{A = 2B}}}. Machine C caps 500 more bottles than Machine A {{{C = A + 500}}}. the three machines cap a total of 40,0

Algebra ->  Equations -> SOLUTION: In one day, Machine A caps twice as many bottles as machine B {{{A = 2B}}}. Machine C caps 500 more bottles than Machine A {{{C = A + 500}}}. the three machines cap a total of 40,0      Log On


   



Question 13285: In one day, Machine A caps twice as many bottles as machine B A+=+2B. Machine C caps 500 more bottles than Machine A C+=+A+%2B+500. the three machines cap a total of 40,000 bottles in a day A+%2B+B+%2B+C+=+40000. How many bottles does each of the machines cap in one day?
Answer by akmb1215(68) About Me  (Show Source):
You can put this solution on YOUR website!
I have added the equations to your question. The three equations you have to work with are A+=+2B....C+=+A+%2B+500...and A+%2B+B+%2B+C+=+40000. To solve, you first need to solve A=2B for B so that you can plug it into the last equation. Once you do this, you get B=%281%2F2%29A, which is the same as B=.5A. Now you can plug this and the other equation in to get A+%2B+.5A+%2B+A+%2B+500+=+40000. Combine like terms to get 2.5A+%2B+500+=+40000. Solve to get 2.5A+=+35000 and then finally A+=+14000. To get B and C, simply plug in A to the original equations: 14000+=+2B....B = 7000. C+=+14000+%2B+500....C = 14500.