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Vikentia [17]
4 years ago
11

If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5 1/2% annual interest to ensure that

the interest he receives each year is 4 1/2% of the total amount invested ?
Mathematics
1 answer:
pogonyaev4 years ago
5 0

Step \; 1: \; Assing \; variable \; for \; the \; unknown \; that \; we \; need \; to \; find.\\Let \; x \; be \; additional \; money \; invested

Step \; 2: \; Use \; the \; appropriate \; formula \; of \; simple \; interest \; set \; up \; an \; equation\\Interest \; earned \; each \; year = \; Amount \; invested \times annual \; rate \; of \; interest\\\\Amount \; invested \; in \; 4 \% \; rate \; of \; interest=\$4500\\Amount \; invested \; in \; 5\frac{1}{2}\% \; rate \; of \; interest= \$x\\Amount \; invested \; totally \; in \; 4\frac{1}{2}\% \; rate \; of \; interest = \$(4500+x)

Interest \; earned \; in \; 4\% \; interest \; rate\\ = \; 4500(4\%)=180\\Interest \; earned \; in \; 5\frac{1}{2}\% \; interest \; rate\\ = x(5\frac{1}{2}\%)=0.055x\\Interest \; earned \; totally \; in \; 4\frac{1}{2}\% \; interest \; rate = (4500+x)(4\frac{1}{2}\%)\\=0.045(4500+x)

\\\\So, \; the \; equation \; would \; be:\\180+0.055x=0.045(4500+x)

Step \; 1: \; Distribute \; 0.045 \; in \; the \; right \; side\\180+0.055x=202.5+0.045x\\\\Step \; 2: \; Subtract \; 0.045x \; and \; 180 \; on \; both \; sides \; to \; get \; x \; alone\\0.055x-0.045x=202.5-180\\\\Step \; 3: \; Combine \; Like \; Terms\\0.01x=22.5\\\\Step \; 4: Divide \; 0.01 \; on \; both \; sides\\\frac{0.01x}{0.01}=\frac{22.5}{0.01}\\\\Step \; 5: \; Simplifying \; fraction \; on \; both \; sides\\x=2250

\underline{Conclusion:}\\Ben \; should \; invest \; additional \; money \; of \; \$2250

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Shtirlitz [24]

Answer: The equation is y = 0.25/(x - 4) + 3

Step-by-step explanation:

If we have a function y = f(x)

A compression means that we multiply the function by a factor smaller than 1.

Then the vertical compression by a factor of 0.25 is:

y = 0.25*f(x)

a translation by A units to the right, means that we need to valuate the function in x - A.

So now we have:

y = 0.25*f(x - 4)

A translation in the y-axis means that we need to add a constant to the equation, then if we tralate it by 3 units up, we have:

y = 0.25*f(x - A) + 3

Then, if f(x) = 1/x

Our new equation is:

y = 0.25/(x - 4) + 3

8 0
3 years ago
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10% of X is 20 what is 23% of X
velikii [3]

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46

Step-by-step explanation:

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23%*200=46

6 0
3 years ago
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9966 [12]
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Henry counted 350 lockers in his school. Hayley counted 403 lockers in her school. How does the 3 in 350 compare to the 3 in 403
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What is the value of w?
sergeinik [125]

Answer:  Most likely, the value of w is 5 units.

Step-by-step explanation: P = 2L + 2w

If the perimeter is 28, the side lengths must be less than 14, otherwise there is no width, just two lines on top of one another.

If the width is 7, then all four sides would be 7 units, and <u>that would create a square</u>-- which is a type of rectangle-- but probably not what this question is about.

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