World Problem Helpp

[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]

Please do not post the same thing twice! I understand that you did not like the formatting but it was still readable!

[Guest]

<a href="https://www.chalokhareeden.in/2020/07/10_18.html/">a=5250,b=11000,c=33000</a>

[Guest]

A=5250
b=11000
c=33000

https://www.chalokhareeden.in/2020/07/10_18.html

[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?

Let a be the amount a invested, b the amount B invested, and c be the amount C invested.
Now, write each statement as an equation. Since we want to find 3 values, a, b, and c we need three equations.

"A, B, and C invested \$47000". So a+ b+ c= 47000.

"B puts in \$500 more than twice as much as A." "Twice as much as A" is 2a. $500 more is 2a+ 500. b= 2a+ 500.

"C puts in three times as much as B." "Three times as much as B" is 3b. c= 3b.

So we have the three equations, a+ b+ c= 4700, b= 2a+ 500, and c= 3b. Basically, we want to reduce from three equations in three unknowns to one equation in one unknown. We can do that by replacing b and c in the first equations with their equivalent in a. "b" is easy because we have b= 2a+ 500. "c" is a little harder. c= 3b and, since b= 2a+ 500, c= 3(2a+ 500)= 6a+ 1500. a+ b+ c= a+ (2a+ 500)+ (6a+ 1500)= 9a+ 2000= 4700. To solve that first subtract 2000 from both sides to get 9a= 2700. Then divide by 9: a= $300.

Don't forget to answer the original question. Since a= $300, b= 2a+ 500= 600+ 500= $1100, and c= 3b= 3(1100)= $3300.

And, of course, check your answer in terms of the original problem.
"Three man: A, B, C, invested $47,000 in business."
a+ b+ c= 300+ 1100+ 3300= 1400+ 3300= 47000. Yes, that checks.

"B puts in $500 more than twice as much as A."
a= \$300 so twice as much is \$600 and \$500 more is \$1100. Yes, b= $1100.

"C puts in three times as much as B."
b= \$1100 so three times as much is is \$3300. Yes, c= $3300.