For the following exercise, create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer’s Rule.
65. At a women's prison down the road, the total number of inmates aged 20 - 49 totaled 5,525. This year, the 20 - 29 age group increased by 10%, the 30 - 39 age group decreased by 20%, and the 40 - 49 age group doubled. There are now 6,040 prisoners. Originally, there were 500 more in the 30-39 age group than the 20-29 age group. Determine the prison population for each age group last year.
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