Amuseum borrows $2,000,000 at simple annual interest to purchase new exhibits. let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. you do not have to solve the system.

Step-by-step explanation:

Total amount borrowed by the museum is $2000000

Let x represent the amount borrowed at 7%

Let y represent the amount borrowed at 8.5%

Let z represent the amount borrowed at 9.5%.

The formula for simple interest is

l = PRT/100

Where

I = interest

P = principal

R = rate

T = time

For a Pincipal of $x borrowed at a rate of 7% and the time is 1 year,

the simple interest would be expressed as

I = (x × 7 × 1)/100 = 0.07x

Fora Principal of $y borrowed at a rate of 8.5% and a duration of 1 year, the simple interest would be expressed as

I = (x × 8.5 × 1)/100 = 0.085y

For a Principal of $z borrowed at rate of 9.5% and a duration of 1 year,

the simple interest would be expressed as

I = (x × 9.5 × 1)/100 = 0.095z

The total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. This means that

y = 4z

The total annual interest would be expressed as

169750 = 0.07x + 0.085×4z + 0.095z

169750 = 0.07x + 0.34z + 0.095z

169750 = 0.07x + 0.435z

The museum borrowed $2,000,000 at simple annual interest. It means that

x + y + z = 2000000

Since y = 4z , then

x + 4z + z = 2000000

x + 5z = 2000000

So the equations are

x + 5z = 2000000

0.07x + 0.435z = 169750

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square