SOLUTION: There are bolts and nuts in a box. The number of bolts are 66 times as many as nuts {{{B = 66N}}}. If 20 more nuts are put in the box, there will be only 36 times as many bolts a

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: There are bolts and nuts in a box. The number of bolts are 66 times as many as nuts {{{B = 66N}}}. If 20 more nuts are put in the box, there will be only 36 times as many bolts a      Log On


   

Question 13169: There are bolts and nuts in a box. The number of bolts are 66 times as many as nuts B+=+66N. If 20 more nuts are put in the box, there will be only 36 times as many bolts as nuts B+=+36%28N+%2B+20%29. How many bolts are in the box?
Answer by akmb1215(68) About Me  (Show Source):
You can put this solution on YOUR website!
You need to first assign variables for the nuts and bolts. I am going to use N for nuts and B for bolts.
I have added equations to your question to describe the sentences.
Since you know that B = 66N, and you also know that B = 36(N + 20), you can set these two equations equal to one another. Therefore, you get 66N+=+36%28N+%2B+20%29.
To solve this, use the distributive property to distribute the 36 across the N+20 to get 66N+=+36N+%2B+720. Move 36N to the left side of the equation by subtracting it from both sides of the equation to get 30N+=+720. Solve by dividing by 30. N=24.
To solve for B, plug in N=24 to the first original equation and solve. B+=+66%2824%29; B = 1,584