Jon invested a total of $40,000 in 3 different bank accounts. One pays an annual interest rate of 3%, the second account pays 5% annual interest and the third account pays 6% annual interest. In one year, Jon earned a total of $1960 in interest from these 3 accounts. If Jon invested $8000 more in the account that pays 5% interest than the account that pays 6% interest. Find the amount that she invested in each amount.
(I have been having trouble solving this problem, can someone help me solve this step by step. THANK YOU.)
let x be 3%, y be 5%, and z be 6%
x + y + z = 40000
3 x + 5 y + 6 z = 196000
y = z + 8000
use the 1st two equations to eliminate x
then substitute for y to find z
substitute back to find x and y
To solve this problem step by step, let's assign variables to the unknowns.
Let X be the amount invested in the account that pays 3% interest.
Let Y be the amount invested in the account that pays 5% interest.
Let Z be the amount invested in the account that pays 6% interest.
We can set up two equations based on the given information:
Equation 1: X + Y + Z = $40,000 (since the total amount invested is $40,000)
Equation 2: 0.03X + 0.05Y + 0.06Z = $1960 (since Jon earned $1960 in interest)
Now, we need to solve these equations simultaneously to find the values of X, Y, and Z.
First, let's simplify Equation 2 by multiplying all terms by 100 to eliminate decimals:
0.03X + 0.05Y + 0.06Z = $1960
Multiply both sides by 100:
3X + 5Y + 6Z = $196000
Now we have the following system of equations:
Equation 1: X + Y + Z = $40,000
Equation 2: 3X + 5Y + 6Z = $196,000
To solve this system, we can use substitution or elimination. Let's use substitution.
From the given information, we know that Y = Z + $8000. We can substitute this into Equation 1:
X + (Z + $8000) + Z = $40,000
Simplifying,
X + 2Z + $8000 = $40,000
X + 2Z = $32,000
X = $32,000 - 2Z
Now we can substitute the value of X in Equation 2:
3X + 5Y + 6Z = $196,000
3($32,000 - 2Z) + 5Y + 6Z = $196,000
96,000 - 6Z + 5Y + 6Z = $196,000
96,000 + 5Y = $196,000
5Y = $100,000
Y = $20,000
Now we have the value of Y. To find Z, we can use Y = Z + $8000:
$20,000 = Z + $8000
Z = $20,000 - $8000
Z = $12,000
Finally, we can substitute the values of X, Y, and Z into Equation 1 to find X:
X + Y + Z = $40,000
X + $20,000 + $12,000 = $40,000
X = $40,000 - $20,000 - $12,000
X = $8,000
Therefore, Jon invested $8,000 in the account that pays 3% interest, $20,000 in the account that pays 5% interest, and $12,000 in the account that pays 6% interest.