Investment A brokerage house offers three stock portfolios for its clients. Portfolio I consists of 10 blocksof common stock, 2 municipal bonds, and 3 blocks ofpreferred stock. Portfolio II consists of 12 blocks ofcommon stock, 8 municipal bonds, and 5 blocks ofpreferred stock. Portfolio III consists of 10 blocksof common stock, 6 municipal bonds, and 4 blocksof preferred stock. A client wants to combine theseportfolios so that she has 180 blocks of common stock,140 municipal bonds, and 110 blocks of preferredstock. Can she do this? To answer this question, letx equal the number of units of portfolio I, y equalthe number of units of portfolio II, and z equal thenumber of units of portfolio III, so that the equation10x + 12y + 10z = 180 represents the total numberof blocks of common stock.a. Write the remaining two equations to create a system of three equations.b. Solve the system of equations, if possible.
Investment A brokerage house offers three stock portfolios for its clients. Portfolio I consists of 10 blocks
of common stock, 2 municipal bonds, and 3 blocks of
preferred stock. Portfolio II consists of 12 blocks of
common stock, 8 municipal bonds, and 5 blocks of
preferred stock. Portfolio III consists of 10 blocks
of common stock, 6 municipal bonds, and 4 blocks
of preferred stock. A client wants to combine these
portfolios so that she has 180 blocks of common stock,
140 municipal bonds, and 110 blocks of preferred
stock. Can she do this? To answer this question, let
x equal the number of units of portfolio I, y equal
the number of units of portfolio II, and z equal the
number of units of portfolio III, so that the equation
10x + 12y + 10z = 180 represents the total number
of blocks of common stock.
a. Write the remaining two equations to create a system of three equations.
b. Solve the system of equations, if possible.
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