Formulate but do not solve the problem.
Michael Perez has a total of $1802 on deposit with two savings institutions. One (x) pays interest at a rate of 6% per year, whereas the other (y) pays interest at a rate of 8% per year. If Michael earned a total of $117 in interest during a single year, how much does he have on deposit in each institution?
= 117
= 1802
$X in acc. 1.
$Y in acc. 2.
Eq1: 0.06X + 0.08Y = 117.
Eq2: X + Y = 1802.
Multiply Eq1 by 100 and Eq2 by -6 and get:
6X + 8Y = 11700
-6X - 6Y = -10812
Add the Eqs:
2Y = 888
Y = $444 in acc. 2.
X + 444 = 1802
X = 1802 - 444 = $1358 in acc. 1.
Let's assume that the amount of money Michael has on deposit in the first institution (x) is "a" dollars, and the amount of money he has on deposit in the second institution (y) is "b" dollars.
We can set up a system of two equations based on the given information:
Equation 1: The total amount of money Michael has on deposit is $1802.
a + b = 1802
Equation 2: The total interest Michael earned in a single year is $117.
0.06a + 0.08b = 117
Now we have a system of two equations with two variables. From here, we can solve these equations to find the values of "a" and "b."