Question 1072150
let:


a = investment in bonds.
b = investment in CDs.
c = investment in mortgages.


total investment is equal to 70,000.


a + b + c = 70,000


total interest is equal to 6,430.


.09 * a + .07 * b + .10 * c = 6,430.


investment in bonds and CDs must be equal to investment in mortgages.


a + b = c


you have 2 equations that needs to be solved simultaneously.


they are:


a + b + c = 70,000


.09 * a + .07 * b + .10 * c = 6,430.


you are given that a + b = c


you can use this information to reduce the number of unknown variables that have to be solved.


replace c with a + b in both equations and you get:


a + b + c = 70,000 becomes a + b + a + b = 70,000 which becomes 2 * a + 2 * b = 70,000.


.09 * a + .07 * b + .10 * c = 6,430 becomes .09 * a + .07 * b + .10 * (a + b) = 6,430 which becomes .09 * a + .07 * b + .10 * a + .10 * b = 6,430 which becomes .19 * a + .19 * b = 6,430.


your 2 equations now become:


2 * a + 2 * b = 70,000


.19 * a + .17 * b = 6,430


in the first equation, solve for a to get:


a = 35,000 -b


in the second equation, replace a with 35,000 - b to get:


.19 * (35,000 - b) + .17 * b = 6,430.


simplify to get:


6,650 - .19 * b + .17 * b = 6,430.


combine like terms to get:


6,650 - .02 * b = 6,430


solve for b to get b = 220 / .02 = 11,000


since a = 35,000 - b, you get a = 24,000


since c = a + b, you get c = 35,000


you can confirm by replacing a with 24,000 and b with 11,000 and c with 35,000 in the original equations to see if they are true.


the original equations are:


a + b + c = 70,000


.09 * a + .07 * b + .10 * c = 6,430.


replace a with 24,000 and b with 11,000 and c with 35,000 to get:


24,000 + 11,000 + 35,000 = 70,000 which becomes 70,000 = 70,000 which is true.-


.09 * 24,000 + .07 * 11,000 + .10 * 35,000 = 6,430 which becomes 6,430 = 6,430 which is true.


both original equations are true, so the solution is good.


you were asked how much should be invested in bonds.


the answer is 24,000.