A man has $290,000 invested in three properties. One earns 12%, one 10% and one 8%. His annual income from the properties is $27,600 and the amount invested at 8% is twice that invested at 12%. (a) How much is invested in each property?

12% property $

10% property $

8% property $

(b) What is the annual income from each property?

12% property $

10% property $

8% property $

Step-by-step explanation:

let amount invested at 12%=x

amount invested in 10 %=y

amount invested in 8 %=z

z=2x

x+y+z=290,000

x+y+2x=290,000

3x+y=290,000  

multiply by 5

15x+5y=1,450,000  ... (1)

12/100 x+10/100 y+8/100 z=27,600

12x+10 y+8z=2,760,000

6x+5y+4z=1,380,000

6x+5y+4(2x)=1,380,000

14x+5y=1,380,000   ... (2)

(1)-(2) gives

x=1,450,000-1,380,000=70,000

z=2(70,000)=140,000

70,000+y+140,000=290,000

y+210,000=290,000

y=290,000-210,000=80,000

invested in 12 %=$ 70,000

invested in 10 %=$ 80,000

invested in 8 %=$ 140,000

(b)

annual income from 12 %=12/100 ×70,000= $8,400

annual income from 10 % =10/100×80,000=$ 9,600

annual income from 8 %=8/100×140,000= $11,200

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.