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Savatey [412]
11 months ago
13

A total of $7000 is invested: part at 8% and the remainder at 12%. How much is invested at each rate if the annual interest is $

580?
Mathematics
1 answer:
Ivahew [28]11 months ago
4 0

We invested $7000 invested in two accounts, we don't know how much exactly is in each account, therefore we will assign variables to these amounts. The amount invested in the "8%" account is "x", while the other one is "y". The sum of these two numbers must be equal to $7000, therefore:

x+y=7000

The sum of interest of each account should be equal to 580, therefore:

0.08\cdot x+0.12\cdot y=580

We need to solve the system in order to determine the values.

\begin{gathered} \begin{cases}x+y=7000 \\ 0.08x+0.12y=580\end{cases} \\ \begin{cases}-0.12x-0.12y=-840 \\ 0.08x+0.12y=580\end{cases} \\ -0.04x=-260 \\ x=\frac{-260}{-0.04}=6500 \\  \end{gathered}

Now we can replace the value of "x" in the first equation to determine the value of "y".

\begin{gathered} 6500+y=7000 \\ y=7000-6500 \\ y=500 \end{gathered}

The values are 6500 in the 8% account and 500 in the 12% account.

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Answer: 12.5\ ft

Step-by-step explanation:

Given

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3 years ago
Two integers, a and b, have a product of 36. What is the least possible sum of a and b?
Minchanka [31]
<h3>Answer:  12</h3>

==============================================================

Explanation:

The two integers multiply to 36, so,

ab = 36

which solves to

a = 36/b

Then we want to add the numbers such that we get the smallest possible result.

a+b = (36/b)+b

So we want (36/b)+b to be as small as possible.

Let's say we replace b with x and we consider this function

f(x) = (36/x) + x

The goal is to find when f(x) is smallest, ie, we want to minimize the function.

If we were to graph out the function, we get the curve shown below.

To make things easier, we'll only focus on positive values of x.

The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.

So the input x = 6 leads to the smallest output f(x) = 12.

This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.

In short, a = 6 and b = 6.

----------------------

As a check,

a*b = 6*6 = 36

a+b = 6+6 = 12

We can make a table of various values to help confirm that 12 is the smallest sum.

Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.

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Andrew is showing his work in simplifying -4.5 + 4.2 + 5.6 - 7.3. Identify
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Answer:

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