Travis has a total of $6,000 invested in two accounts. The total amount of interest he earns from the accounts in the first year is $420. If one account pays 6% per year and the other pays 9% per year, how much did he invest in each account?
Well, let's solve this money mystery, shall we? Let's call the amount Travis invested at 6% "x" and the amount he invested at 9% "y". We know that the total amount invested is $6,000, so we can write the equation: x + y = 6000.
Now let's move on to the interest part. Travis earned $420 in interest for the first year. For the 6% account, he earned x * 0.06, and for the 9% account, he earned y * 0.09. So we can write the second equation: 0.06x + 0.09y = 420.
Now we have a system of two equations:
x + y = 6000
0.06x + 0.09y = 420
To make things more fun, I'll use my clown logic to solve it!
Let's start by multiplying the second equation by 100 to get rid of those pesky decimals:
6x + 9y = 42000
Now, let's solve the system using any method you prefer, like substitution or elimination. Since I'm a playful bot, let's use elimination!
We'll multiply the first equation by -6 to make the x terms cancel out:
-6(x + y) = -6(6000)
-6x - 6y = -36000
Now we have:
-6x - 6y = -36000
6x + 9y = 42000
When we add these two equations together, the x terms disappear:
3y = 6000
Divide both sides by 3, and voila:
y = 2000
Now, substitute this value of y into either equation, like the first one:
x + 2000 = 6000
x = 4000
So, Travis invested $4,000 at 6% and $2,000 at 9%. That's one financially savvy clown right there!
Let's assume Travis invested x dollars in the account that pays 6% interest and y dollars in the account that pays 9% interest.
According to the problem, Travis has a total of $6,000 invested in the two accounts, so we can write the equation:
x + y = 6,000 ----(1)
The total amount of interest Travis earns from the accounts in the first year is $420. We know that the account that pays 6% interest yielded x * 0.06 dollars in interest, and the account that pays 9% interest yielded y * 0.09 dollars in interest. So we can write the equation:
0.06x + 0.09y = 420 ----(2)
To solve the system of equations, we can use substitution or elimination. I will use the substitution method.
Let's solve equation (1) for one variable:
x = 6,000 - y
Substitute this value of x into equation (2):
0.06(6,000 - y) + 0.09y = 420
Distribute and simplify:
360 - 0.06y + 0.09y = 420
Combine like terms:
0.03y = 60
Divide both sides by 0.03:
y = 2,000
Now substitute this value of y back into equation (1) to find x:
x + 2,000 = 6,000
x = 6,000 - 2,000
x = 4,000
Therefore, Travis invested $4,000 in the account that pays 6% interest and $2,000 in the account that pays 9% interest.
To solve this problem, let's assume that Travis invested an amount "x" in the account that pays 6% interest and "6000 - x" in the account that pays 9% interest.
Now, let's calculate the interest earned from each account.
The interest earned from the account that pays 6% interest is given by the formula:
(6/100) * x = 0.06x
Similarly, the interest earned from the account that pays 9% interest is given by the formula:
(9/100) * (6000 - x) = 0.09(6000 - x) = 540 - 0.09x
According to the problem, the total interest earned from both accounts is $420. So we can set up the equation:
0.06x + 540 - 0.09x = 420
To solve this equation, combine like terms:
-0.03x + 540 = 420
Subtract 540 from both sides:
-0.03x = -120
Divide by -0.03:
x = -120 / -0.03
x = 4000
So, Travis invested $4000 in the account that pays 6% interest.
To find the amount invested in the other account, substitute this value back into the equation:
6000 - x = 6000 - 4000 = 2000
Therefore, Travis invested $2000 in the account that pays 9% interest.