a total of 38,000 is invested in two municipal bonds that pay 4.75% and 5.25% simple interest. The investor wants an annual interest income of $1925 from the investments. What amount should be invested in the 4.75% bond?

$14,000 should be invested in the 4.75% bond

Step-by-step explanation:

We need to find the amount "x" that needs to be invested at 4.75%.

Notice as well that the total to be invested equals $38,000, and therefore, what is going to be invested in the other bond (5.25%) must be "$38,000-x"

We now write the equation for the addition of both interests coming from such investment, recalling the formula for simple interest as : I = P * r * t

Where I = Interest

P = Principal (amount deposited)

r = percent rate in decimal form

t = time (one year)

so for the amount  x on the 4.75% bond, the interest after one year would be:

For the amount ($38000-x on the 5.25% bond, the interest after one year would be:

Then, the addition of both interests would render:

Now, recall that the investor wants this total interest to be $1925, then we can write the following equation and solve for "x":

Therefore, the amount to be deposited in the 4.75% bond should be $14,000

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9