Question 1025670
pLEASE HELP ME I AM SO CONFUSED BEEN OUT OF SCHOOL FOR OVER 30YRS AND NEVER HAD PROBLEMS LIKE THIS

1.Maricopa's Success scholarship fund receives a gift of $ 120000. The money is invested in stocks, bonds, and CDs. CDs pay 4 % interest, bonds pay 2 % interest, and stocks pay 7.7 % interest. Maricopa Success invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 5835 , how much was invested in each account? 

 Maricopa Success invested $      in stocks.
 Maricopa Success invested $      in bonds. 
 Maricopa Success invested $      in CDs. 


2.A chemist has three different acid solutions. The first acid solution contains 25% acid, the second contains 35% and the third contains 55%. He wants to use all three solutions to obtain a mixture of 75 liters containing 45%acid, using 3 times as much of the 55% solution as the 35% solution. How many liters of each solution should be used?

 The chemist should use  

  liters of 25% solution,
  liters of 35% solution, and  
  liters of 55% solution.
<pre>Let amount invested in CDs be C
Then amount invested in bonds = C + 35,000
Thus, amount invested in stocks = 120,000 - (C + C + 35,000), or 120,000 - (2C + 35,000), or 120,000 - 2C - 35,000, or 85,000 - 2C
We then get: .04(C) + .02(C + 35,000) + .077(85,000 - 2C) = 5,835
.04C + .02C + 700 + 6,545 - .154C = 5,835
.04C + .02C - .154C = 5,835 - 7,245
- .094C = - 1,410 
C, or amount invested in CDs = {{{(- 1410)/(- .094)}}}, or {{{highlight_green(matrix(1,1,"$15,000"))}}}
Amount invested in bonds: $15,000 + 35,000, or {{{highlight_green(matrix(1,1,"$50,000"))}}}
Amount invested in stocks: $120,000 - (15,000 + 50,000) = $120,000 - 65,000, or {{{highlight_green(matrix(1,1,"$55,000"))}}}
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2.
Let amount of 35% acid to be mixed, be T
Then amount of 55% acid to be mixed = 3T
Amount of 25% acid to be mixed = 75 - (T + 3T), or 75 - 4T
We then get: .35(T) + .55(3T) + .25(75 - 4T) = .45(75)
.35T + 1.65T + 18.75 - T = 33.75
.35T + 1.65T - T = 33.75 - 18.75
T, or amount of 35% acid to be mixed = {{{highlight_green(matrix(1,2, 15, L))}}}
Amount of 55% acid to be mixed: 3(15), or {{{highlight_green(matrix(1,2, 45, L))}}}
Amount of 25% acid to be mixed: 75 - (15 + 45) = 75 - 60, or {{{highlight_green(matrix(1,2, 15, L))}}}