ms. buxx invested a total of $2000 in two savings accounts. The first account pays 3% interest per year and the second account pays 5% interest per yera. If the interest from both accounts totals $84 per yera, how much is invested in each account?
x = amt at 3%
y = amt at 5%
x + y = 2000
.03x + .05y = 84
solve simultaneously for x, y
give it a try, post if you need for help
x = 800, y = 1200 if you are right
the answer is the first account has 800 and the second account has 1200
I need the steps to this equation
x+y=2000
.03x+.05y=84
x+y=2000
-x -x
y=-x+2000 y=-(800)+2000
.03x+.05(-x+2000)=84 y=1200
.03x+ -.05x +100=84
-.02x+100=84
-100 -100
-.02x=-16
-----------
-.02x
x= 800
Ah, the wonders of banking! Let's solve this puzzle together, shall we?
Let's call the amount invested in the first account "x" and the amount invested in the second account "y". Since the total amount invested is $2000, we have the equation:
x + y = 2000
Now, for the interest earned from each account. The first account earns 3% interest, which we can write as 0.03x. The second account earns 5% interest, expressed as 0.05y. Since the total interest earned is $84, we have another equation:
0.03x + 0.05y = 84
Now, using your favorite method of solving equations (mine is interpretive dance, but let's stick with algebra for now), we can solve this system of equations to find the values of x and y.
Multiplying the first equation by 0.03, we get 0.03x + 0.03y = 60.
Next, subtracting this new equation from the second equation, we get 0.03x + 0.05y - (0.03x + 0.03y) = 84 - 60.
Simplifying further, we have 0.05y - 0.03y = 24.
Combining like terms, we get 0.02y = 24.
And finally, by dividing both sides by 0.02, we find y = 1200.
Now, substitute this value of y back into the first equation to solve for x:
x + 1200 = 2000
Subtracting 1200 from both sides, we have x = 800.
So, Ms. Buxx has $800 invested in the first account and $1200 invested in the second account. Ta-dah!
To solve this problem, we need to set up a system of equations based on the given information. Let's denote the amount invested in the first account as "x" and the amount invested in the second account as "y."
According to the problem, the total amount invested is $2000, so we can write the equation:
x + y = 2000
Next, we need to consider the interest earned from each account. The first account pays 3% interest per year, which means it earns 3% of the amount invested (0.03x) in interest. The second account pays 5% interest per year, which means it earns 5% of the amount invested (0.05y) in interest. The total interest earned is given as $84 per year, so we can write the equation:
0.03x + 0.05y = 84
Now we have a system of equations:
x + y = 2000
0.03x + 0.05y = 84
To solve this system of equations, we can use the substitution or elimination method.
Let's solve it using the substitution method. We can express "x" in terms of "y" using the first equation:
x = 2000 - y
Now, substitute this value of "x" in the second equation:
0.03(2000 - y) + 0.05y = 84
Simplify the equation:
60 - 0.03y + 0.05y = 84
0.02y = 24
y = 24 / 0.02
y = 1200
Now that we have found the value of "y," we can substitute it back into the first equation to find the value of "x":
x + 1200 = 2000
x = 2000 - 1200
x = 800
Therefore, $800 is invested in the first account (which pays 3% interest) and $1200 is invested in the second account (which pays 5% interest).