John inherited 25000 and invest part of it in a money market

John inherited 25,000 and invest part of it in a money market account, part in municipal bonds, and part in a mutual fund. After one year, he received a total of $1620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually, There was 6,000 more invested in the bonds than the mutual funds. Find the amount John invested in each catergory.

a. Clearly define the variables

b. Write a system of equations that represents the situation

c. Solve the system of equations using any method, If you use matric method, include your augumented and solution matrics.

d. Write your final answer in a complete sentence,

4. Consider the relation that pairs the date to the number of text messages you sent on that date.

a. Determine which variable is independent and which is dependent.

b. Explain why the relation is or is not a function

Solution

(a) Let the amount invested in money market = x
the amount invested in bonds = y and
the amount invested in mutual fund = z.

(b) Then
x+y+z= 25000 ...(1)
0.06x + 0.07y+0.08z = 1620...(2)
y = z + 6000 ...(3)

(c) Multiply both sides of (2) by 100,
6x + 7y + 8z = 162000
6x + 7(z+6000) + 8z = 162000 (from (3))
6x + 15z +42000=162000
6x +15z = 120000 ... (4)

Substitute y value from (3) into (1),
x + z+6000+z =25000
x+2z = 19000
x = 19000-2z ...(5)

From (4) and (5)

6(19000-2z) +15z = 120000

114000-12z+15z=120000

3z =6000

z= 6000/3 = 2000

Substitute in (3), y = z+2000 = 6000+2000 = 8000

Substitute z in (5), x = 19000 - 2(2000) = 19000-4000=15000

(d) So,the amount invested in money market = $15000
the amount invested in bonds = $8000 and
the amount invested in mutual fund =$2000