Betty Patterson wants to Invest 15000 If she invests in a mu

Betty Patterson wants to Invest $15000. If she invests in a mutual fund paying 6% interest and a bond paying 7% interest, she will earn $968 in interest a year. How much should she Invest in each? Suppose r varies directly as the square of m,  and inversely as s. If r = 12 when m = 6 and s = 4, find r when m = 9 and s = 16. Solve 6(5 - 4x) + 15x 

Solution

14. Suppose Betty invests $ x in the mutual fund paying 6% interest and $ 10000- x in the bond paying 7 % interest. Then 6/100(x) + 7/100(15000-x) = 968 or, 6x/100 + 1050 -7x/100 = 968 or, 1050- 968 = 7x/100-6x/100 or, x/100 = 82 so that x = 8200. Then 15000-x = 15000-8200= 7800. Thus, Betty invests $ 8200 in the mutual fund paying 6% interest and $ 7800 in the bond paying 7 % interest.

15. r varies as square of m so that r = km² where k is the constant of proportionality. Also, r varies inversely as s so that r = p/s where p is the constant of proportionality. Now, r = 12 when m = 6 so that 12=k*(6)² or, 36k = 12 so that k = 12/36 = 1/3 and hence r = m²/3. When m = 9, we have r = 9²/3 = 81/3 = 27. Further, r = 12 when s = 4 so that 12= p/4 or, p = 12*4 = 48. when s = 16, r = p/16 = 48/16 = 3.

16. We have 6(5-4x)+15x < 3(4+2x) or, 30- 24x+15x < 12+6x or, 30 -12 < 24x -15x +6x or, 15x >18 or x > 18/15 or x > 6/5. Thus x ( 6/5, ).

17. We have 5x/6+4/3 -2x = 5/3 or, (5x/6 – 2x) = (5/3- 4/3) or, -7x/6 = 1/3 or, x = (1/3)*(-6/7) = -2/7