college math professor asked us this question
jack and jill each bought a stationary
# of sheets of paper in each box were the same
# of envelopes were the same
jill wrote letters consisting of 3 pages
jack wrote letters consisting of 1 page
when they wrote all letters jill had 50 envelopes left and jack had 50 sheets of paper left
how many pieces of paper and how many envelopes?
This sounds like a problem that involves solving a pair of simultaneous equations. The trick is to interpret the information you are given so that you can come up with the 2 equations.
Let x = the number of pages Jack and Jill each start with
Let y = the number of envelopes Jack and Jill each start with
The two equations we will solve will be of the form:
# of letters written = # of envelopes used
Jill writes until all her paper is gone and she has 50 envelopes left. She uses 3 pages per letter so she writes x/3 letters. She starts with y envelopes and has 50 left so she uses y - 50 envelopes. Now we can write our first equation:
x/3 = y - 50
Now lets consider Jack. Jack writes until all his envelopes are gone and he has 50 pages left. His letters are one page in length so he writes x - 50 letters. All his envelopes are gone so he used y envelopes. Now we can write our second equation:
x - 50 = y
By substituting x - 50 for y in the first equation we can solve for x. Once we have a value for x, we can substitite it into the second equation to solve for y. Its always a good idea to take another look at the question once you have the solution to see if the numbers you found make sense.
Hope this helps,