Can anyone help me with this question. I think it has something todo with solvin

Question

Can anyone help me with this question. I think it has something todo with solving my eliminating equations in the system. Please showall work and I will definitely rank generously. Thankyou.

A company offers three mutual fund plans for its employees. Plan Iconsists of 4 blocks of common stock and 2 municipal bonds. Plan IIconsists of 8 blocks of common stock, 4 municipal
bonds, and 6 blocks of preferred stock. Plan III consists of 14blocks of common
stock, 6 municipal bonds, and 6 blocks of preferred stock. Anemployee wants
to combine these plans so that she has 84 blocks of common stock,40 municipal
bonds, and 36 blocks of preferred stock. How many units of eachplan does she
need?

Explanation / Answer

The goal is to break down the problem to simple things. Plan 1: 4 common and 2 mun Plan 2: 8 common, 4 mun and 6 pre Plan 3: 14 common, 6 mun, 6 pre
Now 84 = 4x + 8y + 14z (commons)-----(1) 40 = 2x + 4y + 6z (mun)-----(2) 36 = 0z + 6y + 6z (pre)-----(3)
From (3) we have: 36 = 0z + 6y + 6z Manipulating we get: z = 6-y -----(4) sub (4) into (2) 40 = 2x + 4y +36 - 6y 4 = 2x - 2y 2x = 4 + 2y -----(5) Subbing (4) & (5) into (1) We have 84 = 4x + 8y + 14z (commons)-----(1) Now we get: 84 = 8 + 4y + 8y + 14(6-y) 8 = 2y y = 4 :. x = 6 :. z = 2
Edit: Forgot to clearify: x = plan 1 y = plan 2 z = plan 3
Hope this is absolutely clear for you. If not please do postback and I'll try to answer as soon as I can.

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