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Kimberly wants to invest $3,000 in an account that earns 4% annual interest , and x dollars in an account that earns 7% so that on average, she would earn 5.5% interest from both accounts . What would be the equation?

Respuesta :

calculista

Answer:

The linear equation that represent this situation is

(3,000+x)0.055=3,000(0.04)+x(0.07)

The value of x is $3,000

Step-by-step explanation:

Let

x -----> the amount invested in an account that earns 7%

we have that

4%=4/100=0.04

7%=7/100=0.07

The linear equation that represent this situation is

(3,000+x)0.055=3,000(0.04)+x(0.07)

Solve for x

165+0.055x=120+0.07x

0.07x-0.055x=165-120

0.015x=45

x=3,000

adioabiola

The equation of her earnings from both of the accounts is;

120 + 0.07x = 0.055x + 165.

According to the question, Kimberly wants to invest $3,000 in an account that earns 4% annual interest, and x dollars in an account that earns 7%.

For the first account;

  • Total amount = (4% of $3,000) = 0.04 × $3,000

  • Total amount = $120.

Fir the second account;

  • Total amount = (7% of x dollars) = 0.07x

  • Total amount = $0.07x

On the average, she would earn 5.5% interest from both accounts;

Mathematically, we have;

  • 5.5% of $(x + 3000).

  • Total earnings = 0.055x + 165

The equation of the relationship between the accounts is therefore;

  • 120 + 0.07x = 0.055x + 165.

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