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 $258,000, then how many investors contributed $3,000 and how many contributed $6,000?

Answer 1

There are 26 investors which contributed 6,000

And 34 investors which contributed 3,000

Explanation:

You need to set up a two equation problem

`\left \{ {{258,000=6,000y+3,000x} \atop {60=y+x}} \right.`

Now you have to clear "x" or "y" from the second equation:

`y = 60 - x`

And replace on the first equation:

`258,000 = 6,000 (60 - x) + 3,000x\\258,000 = 360,000 - 6,000x + 3,000x\\3,000x = 360,000 - 258,000\\x = 102,000/3,000\\x = 34`

And now you use this "x" vale on the second equation

`60 = y + x\\60 = y + 34\\60 - 34 = y\\y = 26`

There are 26 investors which contributed 6,000

And 34 investors which contributed 3,000