Formulate the situation as a system of two linear equations in two variables. Be

Question

Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question. A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $324,000, then how many investors contributed $4,000 and how many contributed $8,000? x = $4,000 investors y = $8,000 investors

Explanation / Answer

Solution:

Let x be the number of $4,000 investors and

let y be the number of $8,000 investors

As per given condtion

lawyer has found 60 investors for a limited partnership

therefore x +y = 60 ....eqution 1

the partnership raised $324,000

therefore

4000x + 8000y = 324,000 . ...equation 2

Solving above equation by elimination method

STEP 1: Multiply first equation by -4000.

After multiplying we have the following system:

4000x4000y = 240000

4000x+8000y = 324000

STEP 2: add the two equations together to eliminate x from the system.

4000y=84000

STEP 3: find y

y=21

STEP 4: substitute the value for y into the original equation to solve for x.

x+(21)=60

x=39

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