SOLUTION: Mandie has enough sheets of paper to give each of her friends 3 sheets and has 31 sheets left over. Alternatively, she could give each friend 4 sheets and have 9 sheets left over

Algebra ->  Average -> SOLUTION: Mandie has enough sheets of paper to give each of her friends 3 sheets and has 31 sheets left over. Alternatively, she could give each friend 4 sheets and have 9 sheets left over      Log On


   

Question 1140905: Mandie has enough sheets of paper to give each of her friends 3 sheets and has 31
sheets left over. Alternatively, she could give each friend 4 sheets and have 9 sheets
left over. How many sheets of paper does she have?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This problem is to be solved MENTALLY. 


From the condition, an attentive reader can notice momentarily, that the number of friends is 31-9 = 22.


Then the number of sheets is 4*22 + 9 = 88+9 = 97.      ANSWER


CHECK.  22*3+31 = 66 + 31 = 97, the same number.   ! Correct !

Solved. 

Another, formal algebra solution is to write this system of 2 equations


    X - 3*N = 31,     (1)
    X - 4*N =  9,     (2)


where X is the number of sheet and N is the number of friends, and solve it by any way.