Respuesta :
Bax invested a total of $2000 in two simple interest accounts. Account A earns 3% interest and Account B earns 5% interest. Bax earned a total of $75 interest after one year. How much did Bax invest in each account?
Let, The amount invested in Account A=x
Then, the amount invested in Account B=2000-x
The formula of Simple Interest =[tex] \frac{Principle*Rate*Time}{100} [/tex]
Interest earned in Account A in 1 year=[tex] \frac{x*3*1}{100} [/tex]
Interest earned by Account A=[tex] \frac{3x}{100} [/tex]
Interest earned in Account B in 1 year=[tex] \frac{(2000-x)*5*1}{100} [/tex]
Interest earned by Account B=[tex] \frac{5(2000-x)}{100} [/tex]
Total Interest Earned= Interest earned by Account A+ Interest earned by Account B
Total Interest Earned=[tex] \frac{3x}{100} [/tex]+[tex] \frac{5(2000-x)}{100} [/tex]
75=[tex] \frac{3x}{100} [/tex]+[tex] \frac{10000-5x)}{100} [/tex]
75=[tex] \frac{3x+10000-5x)}{100} [/tex]
Multiply by 100 on both sides
75*100=[tex] \frac{100(10000-2x))}{100} [/tex]
7500=10000-2x
Let us subtract 7500 from both sides
7500-7500=10000-7500-2x
0=2500-2x
Adding 2x on both sides, we get
0+2x=2500-2x+2x
2x=2500
To solve for x, divide by 2 on both sides
2x/2=2500/2
x=1250
So, The Amount invested in Account A= $1250
The Amount invested in Account B= $2000-1250=$750
