Question 126501
1. Define values for the number if bills of each denomination (given in the problem):
Let x = number of $100 bill
Let 3x = number of $50 bills
Let 12x = number of $20 bills
Let 4x = number of $1 bills
Let x+9 = number of $5 bills 

2. Define values for the dollar values of each denomintion (multiply variable from step 1 by the value of the denomiation):
Let 100x = value of all $100 bills
Let 50(30x) = 150x = value of all $50 bills
Let 20(12x) = 240x = value of all $20 bills
Let 1(4x) = 4x = value of all $1 bills
Let 5(x+9) = 5x+45 = value of all $5 bills

3. Set up the equation:
{{{100x + 150x + 240x + 4x + 5x + 45 = 1043}}}
4. Simplify and solve:
{{{499x + 45 = 1043}}}
{{{499x = 998}}}
{{{x = 2}}}

5. Substitute x = 2 for all variables in step 1 to determine number of each denomination Malcolme has:
{{{x = 2}}} $100 bills
{{{3x = 3(2) = 6}}} $50 bills
{{{12x = 12(2) = 24}}} $20 bills
{{{4x = 4(2) = 8}}} $1 bills
{{{x + 9 = (2) + 9 = 11}}} $5 bills

6. Check: Multiply the number of each bill by its face value and sum:
{{{2(100) + 6(50) + 24(20) + 8(1) + 11(5) = 1043}}}
{{{1043 = 1043}}}