History Bookmarks People Window Help al Pole Mo NW The Unive

History Bookmarks People Window Help al Pole (Mo NW The University of Akron Log x E McGraw-Hill Connect Math x a Hybridizatio Animal Pole, Vegetal Pole (Molecular Biology) Previous 11 12 13 14 Question 14 of 14 (0.7 points) View problem in a pop-up 7.1 Section Exercise 59, 60 Model the problem using a system of line equations. Then solve using the augmented matrix. The trustee of a unions pension fund has invested funds in three ways: a savings fund paying 8% annual interest, a money market fund paying 4%, and government bonds paying 7%. Find the amount invested in each ifthe interest earned after one year is so.124 million and the amount in government bonds is so.2 million more than twice the amount in money market funds. The total amount invested is S1.8 million. Part 1 out of 3 The amount invested in a savings fund was s million. CHECK NEXT

Solution

Let the amount invested in Saving fund = $x million

                                             in Money market fund = $y million

                                             in Government bond = $z million

Total invested amount is $1.8 million

So, x+y+z=1.8 .....(equation 1)

Interest earned from saving fund in a year = amount invested * rate of interest = $0.08x million

Interest earned from money market fund = $0.04y million

Interest earned from government bond = $0.07z million

Total interest earned in a year is $0.124 million, which means,

0.08x+0.04y+0.07z=0.124 or 8x+4y+7z=12.4 (by multiplying both sides by 100).....(equation 2)

The question also states that the amount in government bond is $0.2 million more than twice the amount in money market funds, which means

z=2y+0.2 ......(equation 3)

Here we need to find x, (amount invested in savings fund)

Plug z=2y+0.2 in equation 2, so we get

8x+4y+7(2y+0.2)=12.4

or 8x+4y+14y+1.4=12.4

or 8x+18y=11.......(equation 4)

Now plug z=2y+0.2 into equation 1, and we get

x+y+2y+0.2=1.8

x+3y=1.6 ....(equation 5)

Multiply (equation 5) with -6 and add to equation 4

   8x+18y= 11

-6x-18y=-9.6

__________

2x = 1.4

x=0.7

So amount invested in Saving fund is $0.7 million