Michael has a total of $2000 on deposit with two saving institutions. One pays interest at the rate of 6% per year whereas the other pays interest at a rate of 8% per year. If Michael earned a total of $144 in interest during a single year, how much did he deposit in each institution? [Use the substitution method to solve]
X=120 Y=160
Y= 144-X
Let's assume that Michael deposited $x in the first institution and $y in the second institution.
According to the given information, the interest rate at the first institution is 6% per year, and the interest rate at the second institution is 8% per year.
The interest earned at the first institution would be (6/100) * x = 0.06x dollars per year. Similarly, the interest earned at the second institution would be (8/100) * y = 0.08y dollars per year.
The total interest earned by Michael in a single year is $144. Therefore, we can write the equation:
0.06x + 0.08y = 144
Now, we also know that the total amount deposited by Michael is $2000. Hence, another equation can be written as:
x + y = 2000
We can solve this system of equations using the substitution method.
Let's solve the second equation for x:
x = 2000 - y
Now substitute the value of x in the first equation:
0.06(2000 - y) + 0.08y = 144
Simplify the equation:
120 - 0.06y + 0.08y = 144
Combine like terms:
0.02y = 144 - 120
0.02y = 24
Divide both sides of the equation by 0.02:
y = 24 / 0.02
y = 1200
Now substitute the value of y back into the second equation to find x:
x + 1200 = 2000
x = 2000 - 1200
x = 800
Therefore, Michael deposited $800 in the first institution and $1200 in the second institution.
To solve this problem using the substitution method, we need to set up a system of equations based on the given information.
Let's say Michael deposited x dollars in the institution that pays 6% interest, and y dollars in the institution that pays 8% interest.
The interest earned from the first institution can be calculated as 6% of x, which is 0.06x. Similarly, the interest earned from the second institution is 8% of y, which is 0.08y.
According to the problem, Michael earned a total of $144 in interest, so we can write the first equation:
0.06x + 0.08y = 144
Now, we also know that the total amount deposited by Michael is $2000. This gives us the second equation:
x + y = 2000
We have a system of two equations with two variables. To solve this system using the substitution method, we can solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation for x:
x = 2000 - y
Now, substitute x in the first equation with 2000 - y:
0.06(2000 - y) + 0.08y = 144
Distribute 0.06 to both terms inside the parentheses:
120 - 0.06y + 0.08y = 144
Combine like terms:
0.02y = 24
Divide both sides by 0.02:
y = 1200
Now, substitute the value of y back into the second equation to find x:
x + 1200 = 2000
x = 2000 - 1200
x = 800
Therefore, Michael deposited $800 in the institution that pays 6% interest, and $1200 in the institution that pays 8% interest.
Let the amount earning 6% be X and the amount earning 8% be Y. You have to solve these two equations in two unknowns.
X + Y = 2000
0.06 X + 0.08 Y = 144
Substitute 2000 -X for Y in the second equation and solve the resulting equation for X.
0.06X + 0.08(2000 - X) = 144
160 -144 = 0.02 X
X = $800
Y = 2000 - X = $1200