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Dafna1 [17]
3 years ago
10

The sum of two numbers is 114. The second number is 24 less than twice the first number. Find the numbers.

Mathematics
1 answer:
mars1129 [50]3 years ago
4 0

Answer:

46 and 68

Step-by-step explanation:

so let the first number=x

the second number= 2x-24 since 24 less than twice the first number

then

2x-24+x=114

simplify

3x=114+24

3x=138

x=46

2x-24= 68

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David’s bank offers a 36-month Certificate of Deposit (CD) with an APR of 2.25%. Use the compound interest formula to answer the
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Using compound interest, it is found that:

a) A(8) = 2389.66

b) t = 31.15

c) P = 1870.85

Compound interest:

A(t) = P\left(1 + \frac{r}{n}\right)^{nt}

  • A(t) is the amount of money after t years.  
  • P is the principal(the initial sum of money).  
  • r is the interest rate(as a decimal value).  
  • n is the number of times that interest is compounded per year.  
  • t is the time in years for which the money is invested or borrowed.

In this problem:

  • The APR is of 2.25%, hence r = 0.0225.
  • No information about the number of compounding per year, hence n = 1.

Item a:

P = 2000, hence:

A(t) = P\left(1 + \frac{r}{n}\right)^{nt}

A(8) = 2000\left(1 + \frac{0.0225}{1}\right)^{8}

A(8) = 2389.66

Item b:

A(t) = 4000, hence:

A(t) = P\left(1 + \frac{r}{n}\right)^{nt}

4000 = 2000\left(1 + \frac{0.0225}{1}\right)^{t}

(1.0225)^t = 2

\log{(1.0225)^t} = \log{2}

t\log{1.0225} = \log{2}

t = \frac{\log{2}}{\log{1.0225}}

t = 31.15

Item c:

A(3) = 2000, hence:

A(t) = P\left(1 + \frac{r}{n}\right)^{nt}

2000 = P\left(1 + \frac{0.0225}{1}\right)^{3}

P = \frac{2000}{(1.0225)^3}

P = 1870.85

A similar problem is given at brainly.com/question/24850750

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