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in 2009 a total of R36 000 was invested in two accounts. One account earned 7% annual interest and the other earned 9% .The tota

Akimi4 [234]

a = amount invested at 7%

b = amount invested at 9%

we know the amount invested was ₹36000, thus we know that whatever "a" and "b" are, a + b = 36000. We can also say that

$\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of a}}{\left( \cfrac{7}{100} \right)a}\implies 0.07a~\hfill \stackrel{\textit{9\% of b}}{\left( \cfrac{7}{100} \right)b}\implies 0.09b$

since we know the interest earned from the invested was ₹2920, then we say that 0.07a + 0.09b = 2920.

$\begin{cases} a + b = 36000\\\\ 0.07a+0.09b=2920 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{a + b = 36000\implies \underline{b = 36000-a}}~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.07a~~ + ~~0.09(\underline{36000-a})~~ = ~~2920} \\\\\\ 0.07a+3240-0.09a=2920\implies 3240-0.02a=2920\implies -0.02a=-320 \\\\\\ a=\cfrac{-320}{-0.02}\implies \boxed{a=16000}~\hfill \boxed{\stackrel{36000~~ - ~~16000}{20000=b}}$

5 0

2 years ago

What is 1 7/9 - 4/9?

Lera25 [3.4K]

1 7/9 - 4/9

Convert 1 7/9 to an improper fraction:

16/9 - 4/9

Subtract the numerators together:

12/9

Convert to a whole number:

1 1/3

7 0

3 years ago

Read 2 more answers

X+3y+12+5y it’s confusing and I can’t gwt the answer

Ket [755]

Answer: In your problem you will have to combine liked terms, and you can't combine non-like terms. After you combine your liked terms you will get your answer.

3 0

2 years ago

You purchase a car worth $25077 and make a down payment of $3560. You intend to repay the balance of the car with month end car

zubka84 [21]

Answer:

value of buyout is $4185.74

Step-by-step explanation:

given data

car worth = $25077

down payment = $3560

monthly payment = $336 = 336 × 6 = $2016 per semi annually

time = 5 year = 10 half yearly

rate = 4.04 %

to find out

value of final buyout

solution

we know here loan amount will be 25077 - 3560 = $21517

and we find present value first by formula that is

present value = $\frac{amount(1+r)^t - 1}{r (1+r)^t}$

put here t = 10 and r = $\frac{4.04}{200}$

so

present value = $\frac{2016(1+\frac{4.04}{200})^10 - 1}{r (1+\frac{4.04}{200})^10}$

present value = 18089.96

so

loan unpaid amount is here

loan unpaid amount = 21517 - 18089.96

loan unpaid amount = $3427.04

so

now we calculate value of buyout

that is express as

amount = principal × $(1+r)^{t}$

amount = 3427.04 × $(1+\frac{4.04}{200})^{10}$

amount = 4185.74

so value of buyout is $4185.74

7 0

3 years ago

A baseball collector took inventory of all of his baseball cards along with the value of each card. The box plot represents the

love history [14]

Answer: less than 25%

Step-by-step explanation:

The box plot can be read as follows:

The first black dot is the minimum value.

The first half of the rectangle is the lower quartile.

The line that separates the two rectangles is the median.

The second half of the rectangle is the upper quartile

The final point is the maximum.

Knowing that each quartile represents about the 25% of the elements for the set, we can see that both lower and upper quartile (and the 25% of the elements that come after the upper quartile) cost more than $45.

Then we know that at least the (25% + 25% + 25%) = 75% of the cards in the collection cost more than $45.

And we also have elements that are not in the lower quartile that cost more than $45, but we can not determine the percentage that they represent.

So we can only conclude that more than the 75% of the collection costs more than $45.

Now we want to know the percentage of the baseball cards valued at less than $45.

So if more than 75% is valued at more than $45.

Then less than 25% is valued at less than $25.

8 0

2 years ago