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Neporo4naja [7]
3 years ago
10

Douglas invests money in two simple interest accounts. He invests three times as much in an account paying 14% as he does in an

account paying 5%. If he earns $152.75 in interest in one year from both accounts combined, how much did he invest altogether?
Mathematics
2 answers:
Igoryamba3 years ago
6 0

Answer:

Altogether, he invested $1300.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

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% E_{1} and the earnings from the account paying 5% E_{2}. The principals are P_1 and P_{2}, in which P_{1} = 3P_{2}.

So

E_{1} = P_{1}*0.14t

E_{2} = P_{2}*0.05t

He earns $152.75 in interest in one year from both accounts combined.

This means that

E_{1} + E_{2} = 152.75

I am going to write E_{1} as a function of E_{2} and replace in the first equation, that of E_{1}.

So

E_{1} = 152.75 - E_{2}

E_{1} = P_{1}*0.14t

We also have that

P_{1} = 3P_{2}

So

152.75 - E_{2} = 3*P_{2}*0.14t

In which

E_{2} = P_{2}*0.05t

So

152.75 - P_{2}*0.05t = 0.42P_{2}t

His earnings are after 1 year, so t = 1

152.75 - P_{2}*0.05 = 0.42P_{2}

0.42P_{2} + P_{2}*0.05 = 152.75

0.47P_{2} = 152.75

P_{2} = \frac{152.75}{0.47}

P_{2} = 325

His smaller investment is 325.

P_{1} = 3P_{2} = 3*325 = 975

How much did he invest altogether?

This is P_{1} + P_{2}

P_{1} + P_{2} = 975 + 325 = 1300

Altogether, he invested $1300.

egoroff_w [7]3 years ago
3 0

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

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