Algebra word problem Solving for a variable

Question

I am a number less than 3000. When you divide me by 32, my remainder is 30.  When you divide my by 58, my remainder is 44.  What number am I?

Answer 1

Lets use the remainder theorem.  If we multiply the quotient "Q" by the divisor, then add the remainder to the result, you get the dividend "N".  That dividend is the number you are looking for.

 

32Q + 30 = N              eq1

58Q + 44 = N              eq2

 

You now have a system of equations.  Use the substitution method.

 

32Q + 30 = 58Q + 44

 

 

Solve for Q.

 

32Q - 58Q = 44 - 30

 

-26Q = 14

 

     Q = -7/13

 

 

Plug in this value of Q into any of the equations to get your number.