Charles saves $y. Sharon saves 3 times as much as Charles. Jason saves 50.00 more thN Sharon. How much do they save

A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

5 0

3 years ago

You have a rectangular yard that measures 16 feet Long by 14 feet wide.it id covered in grass except For in the Center,where the

BartSMP [9]

A of the yard= L*l=16*14= 224 feet²

A of the fountain= πR²

d=2R
4=2R

R=4:2=2

A of the fountain= 2²π=4 *3,14= 12,56 feet²

A of the grass portion= 224-12,56= 211,43 feet²

answer d)211,43 feet²

5 0

3 years ago

You unfold chicken wire to make a circular pen. The area of the pen is 78.5 square meters. How many meters of chicken wire do yo

Lelu [443]

Circular pen means you are going to use Area = Pi(r^2).

So 78.5 = pi(r^2). Divide by pi on both sides to get r^2 = 78.5/pi. Take the square root of that to get r or radius = approximately 4.99. If you need an exact answer then use $\sqrt{ \frac{78.5}{ \pi } }$ for the next part because you are not done yet.

Plug whatever R you use into the circumference formula of Circumference = 2(pi)(r).

If you use 4.99, you do 2(pi)(4.99) which is approximately 31.35. If you use the exact answer, you do 2(pi)( $\sqrt{ \frac{78.5}{ \pi} }$ ) which gives you approximately 31.41.

Either way you'll need about 31 meters of chicken wire but the 31.40796 or ~31.41 is closer to the exact answer.

8 0

3 years ago

If k is the incenter of def find each measure

3241004551 [841]

Answer:

https://ohsrehak.weebly.com/uploads/5/4/6/9/54699399/5-1_bisectors_of_triangles_solutions.pdf paste the click

Step-by-step explanation:

3 0

3 years ago

The ratio in fraction of 2.5/8 to 8. 3/4 as a fraction in simplest form

labwork [276]

The answer to your question would be, 22 31/32 because you would multiply 2 5/8 and 8 3/4. To=mutiply. Hope I helped:-)

3 0

3 years ago