word problem help

Question

Mary invested a total of $46,000 in three different bank accounts. One account pays an annual interest rate of 22%, the second account pays 33% annual interest, and the third account pays 55% annual interest. In oneyear, Mary earned a total of $1610 in interest from these three accounts. If Mary invested $5,000 more in the account that pays 33% interest than she did in the account that pays 55% interest find the amount she invested in each account.

Answer 1

x+y+z = 46K, x= amount invested at 22%, y at 33%, z at 55%, K=$1000

y = z +5K, $5000 more invested at 33% than at 55%

.22x +.33y +.55z = 1.61K total interest for all 3 is $1,610 in 1 year

3 equations 3 unknowns

solve by matrix algebra or substitution elimination