Find the amount invested in the first, second, and third account

Question

Mary invested a total of $36,000 in 3 different bank accounts. One account pays an annual interest rate of 3% the second account pays 4% annual interest and the third account pays 5% annual interest. Mary earned a total of $1,490 in interest from these three accounts. if Mary invested $11,000 more in the account that pays 4% interest then she did in the account that pays 5% interest find the amount she invested in each account

Answer 1

X+Y+Z = 36000

Y = Z+11000

0.03X + 0.04Y + 0.05Z = 1490

===== substitutes second equation into first and third equations =================

X + Z+11000 + Z = 36000

0.03X + 0.04(Z + 11000) + 0.05Z = 1490

X + 2Z = 25000

X = 25000 - 2Z

0.03X + 0.09Z + 440 = 1490

0.03X + 0.09Z = 1050

0.03( 25000 - 2Z) + 0.09Z = 1050

750 - 0.06Z + 0.09Z = 1050

750 + 0.03Z = 1050

0.03Z = 300

3Z = 30000

Z = 10000

Y = 21000

X = 5000