business

[Guest]

Hey there, I kindly ask you to help me to solve this world problem and I'm getting nervous..

Three man: A, B, C, invested \$47,000 in business. B puts in \$500 more than twice as much as A, and C puts in three times as much as B. How many dollars each put into the business?

[HallsofIvy]

Hey there, I kindly ask you to help me to solve this world problem and I'm getting nervous..

Three man: A, B, C, invested \$47,000 in business. B puts in \$500 more than twice as much as A, and C puts in three times as much as B. How many dollars each put into the business?

I believe I saw this answered on another board but, for those who are interested here:
Use "a", "b", and "c" to represent the amount, in dollars, that each of these invested. (Many people would use "A", "B", and "C" but, in my mind, those are already used to mean the people, not the amounts.)

Each sentence gives an equation.

A, B, C, invested \$47,000 in business

a+ b+ c= 47000

B puts in \$500 more than twice as much as A,

"twice as much as A" is 2a. \$500 more than that is 2a+ 500.
b= 2a+ 500

and C puts in three times as much as B.

c= 3b

Solve the three equations for a, b, and c:
a+ b+ c= 47000
b= 2a+ 500
c= 3b.

To solve three equations for three values, reduce to one equation in one unknown.
b= 2a+ 500 and c= 3b= 3(2a+ 500)= 6a+ 1500 so the first equation can be written as
a+ b+ c= a+ 2a+ 500+ 6a+ 1500= 9a+ 2000= 47000
Subtract 2000 from both side: 9a= 4500.
Divide both sides by 9: a= 5000.
Then b= 2(5000)+ 500= 10000+ 500= 10500.
c= 3b= 3(10500)= 31500.

You should also state your solution to the original problem clearly (the original problem said nothing about "a", "b", or "c").
A put in \$5000, B put in \$10500, and C put in \$31500.

And you should also check your answers.
"A, B, C, invested \$47,000 in business."
a+ b+ c= 5000+ 10500+ 31500= 15500+ 31500= 47000.

"B puts in \$500 more than twice as much as A"
"Twice as much as A" is 2(5000)= 10000. 500 more than that is 10000+ 500=10500.
That is what B put in.

"C puts in three times as much as B."
3(10500)= 31500.
That is what C put in.

(When I first did this problem, I accidently dropped a "0". If I hadn't checked I would have posted the wrong answer and looked foolish! Always check your work!)

[mycalsuite]

A= $5,000
B=$10,500
C=$31,500
Check: 5000 + 10500 + 31500 = 47000

[Guest]

So, from my point of view, it’s actually not that complicated. A put in a smaller amount, B put in quite a bit more like a little over double what A invested and then C put in a lot, basically three times what B put in. Altogether, it adds up to the $47,000. To me, it makes sense, because it shows how differently the three are sharing the risk, and you can pretty easily figure out how the business shares are divided. You could of course argue whether that’s fair or not, but mathematically it works out.