SOLUTION:
We are going to use the concept of simultaneous equations to answer this question;
x + y = $ 55000 .........................(1)
Recall that;
[tex]\text{Interest = }\frac{PRT}{100}[/tex][tex]\begin{gathered} \frac{x\text{ X 2 X 1}}{100}\text{ + }\frac{y\text{ X 7.5 X 1}}{100}\text{ = \$3135} \\ \\ \frac{2x}{100}\text{ + }\frac{7.5y}{100}\text{ = \$ 3135 (multiply through by 100)} \\ \\ 2x\text{ + 7.5y = \$313500 }\ldots\ldots\ldots\ldots\ldots.........(2) \end{gathered}[/tex]We can now solve the two equations simultaneously
From equation (1);
x = 55000 - y .............................(3)
Substitute equ.3 into equ. 2
2 (55000 - y) + 7.5y = 313,500
110,000 - 2y + 7.5y = 313,500
5.5y = 313,500 - 110,000
5.5y = 203,500 ( divide both sides by 5.5)
y = $37,000
Substitute y = 37,000 into equ 3
x = 55,000 - 37,000 = $18,000
Therefore, x = $18,000 and y = $37,000
The amount invested at 2% is $18,000 and the amount invested at the rate of 7.5% is $ 37,000
