Formulate the situation as a system of two linear equations in two variables. Be
ID: 3167364 • Letter: F
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