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 $3,000 or $6,000. If the partnership raised $240,000, then how many investors contributed $3,000 and how many contributed $6,000?

Explanation / Answer

Let the number of investors contributing $3000 be x

and the number of investors contributing $6000 be y

Then:

x + y = 60 .. eqn 1

3000*x + 6000*y = 240000 … eqn 2

multiply eqn 1 by 3000, they becomes

3000*x + 3000*y = 180000 .. eqn 3

3000*x + 6000*y = 240000 … eqn 2

subtract eqn 3 from eqn 2 to eliminate x

3000*x - 3000*x + 6000*y - 3000*y = 240000 - 180000

3000*y = 60000

y = 20

put this in eqn 1

x + 20 = 60

x = 40

Answer:

number of investors contributing $3000 is 40

and the number of investors contributing $6000 is 20

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