Respuesta :
Answer:
Altogether, he invested $1300.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
He invests three times as much in an account paying 14% as he does in an account paying 5%.
I am going to call the earnings from the account paying 14% [tex]E_{1}[/tex] and the earnings from the account paying 5% [tex]E_{2}[/tex]. The principals are [tex]P_1[/tex] and [tex]P_{2}[/tex], in which [tex]P_{1} = 3P_{2}[/tex].
So
[tex]E_{1} = P_{1}*0.14t[/tex]
[tex]E_{2} = P_{2}*0.05t[/tex]
He earns $152.75 in interest in one year from both accounts combined.
This means that
[tex]E_{1} + E_{2} = 152.75[/tex]
I am going to write [tex]E_{1}[/tex] as a function of [tex]E_{2}[/tex] and replace in the first equation, that of [tex]E_{1}[/tex].
So
[tex]E_{1} = 152.75 - E_{2}[/tex]
[tex]E_{1} = P_{1}*0.14t[/tex]
We also have that
[tex]P_{1} = 3P_{2}[/tex]
So
[tex]152.75 - E_{2} = 3*P_{2}*0.14t[/tex]
In which
[tex]E_{2} = P_{2}*0.05t[/tex]
So
[tex]152.75 - P_{2}*0.05t = 0.42P_{2}t[/tex]
His earnings are after 1 year, so [tex]t = 1[/tex]
[tex]152.75 - P_{2}*0.05 = 0.42P_{2}[/tex]
[tex]0.42P_{2} + P_{2}*0.05 = 152.75[/tex]
[tex]0.47P_{2} = 152.75[/tex]
[tex]P_{2} = \frac{152.75}{0.47}[/tex]
[tex]P_{2} = 325[/tex]
His smaller investment is 325.
[tex]P_{1} = 3P_{2} = 3*325 = 975[/tex]
How much did he invest altogether?
This is [tex]P_{1} + P_{2}[/tex]
[tex]P_{1} + P_{2} = 975 + 325 = 1300[/tex]
Altogether, he invested $1300.
Answer:
Step-by-step explanation:
Let x represent the amount invested in the account paying 14% interest.
Let y represent the amount invested in the account paying 5% interest.
He invests three times as much in an account paying 14% as he does in an account paying 5%. This means that
x = 3y
The formula for simple interest is expressed as
I = (PRT)/100
Considering the account earning 14% interest,
I = (x × 14 × 1)/100 = 0.14x
Considering the account earning 5% interest,
I = (y × 5 × 1)/100 = 0.05y
If he earns $152.75 in interest in one year from both accounts combined, it means that
0.14x + 0.05y = 152.75 - - - - - - - - - -1
Substituting x = 3y into equation 1, it becomes
0.14(3y) + 0.05y = 152.75
0.42y + 0.05y = 152.75
0.47y = 152.75
y = 152.75!0.47
y = 325
x = 3y = 3 × 325
x = $975
Total amount of money invested is
975 + 325 = $1300
