Question 1201076
<br>
The response from the other tutor shows a setup for solving the problem using a single equation; you asked for a solution using a system of equations.<br>
Let x = amount invested at 5%
Let y = amount invested at 7%<br>
(1) The total invested is $2000: x+y = 2000
(2) The total interest is $108: .05x+.07y = 108<br>
One solution method is to solve the first equation for either x or y and substitute in the second equation:<br>
y = 2000-x
.05x+.07(2000-x) = 108<br>
That gives you a single equation in a single variable, like the one shown in the response from the other tutor.<br>
The other standard algebraic method for solving a system of two equations is elimination.  Here is one possible way to do that<br>
x+y = 2000  (the first equation, as it is)
x+1.4y = 2160  (the second equation, multiplied by 20 -- because 20*(.05) = 1)
0.4y = 160
y = 160/0.4 = 400<br>
y = $400 was invested at 7%, so $2000-$400 = $1600 was invested at 5%<br>
ANSWER: $1600 at bank A, $400 at bank B<br>
NOTE:  Solving a problem with formal algebra using a single variable (and therefore a single equation) almost always makes the actual solution easier and faster.  However, a beginning algebra student should understand how to set up and solve the problem using two variables, as this assignment asks you to do.<br>
Second NOTE: If formal algebra is not required, here is a quick and easy way to solve this kind of "2-part mixture" problem.<br>
(1) If all $2000 were invested at 5%, the interest would be $100; if all were invested at 7%, the interest would be $140.
(2) The actual interest, $108, is $8/$40 = 1/5 of the way from $100 to $140.
(3) That means 1/5 of the total was invested at the higher rate.<br>
ANSWER: 1/5 of $2000, or $400, was invested at 7%; the other $1600 at 5%.<br>