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So I stumbled across this math problem:

$1015$ USD is to be shared between $3$ people: Person A, Person B and Person C. Person A gets double of what Person B gets and Person B gets $100$ USD more than Person C

Basically:

$A = 2B$

$B = C + 100$

$A + B + C = 1015$

Can someone please tell me how it's solved, rather than telling me the outcome?

UPDATE: Thank you to people who helped me solve it. What I realized was, that I used the equation C = B - 100 to try to solve the problem. You made me realize that. So thank you.

MathX00
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2 Answers2

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Basically, $A=2B$ and $B=C+100$. We have $$A+B+C =1015$$ $$\Rightarrow 2B+B+(B-100) =1015$$ because $B+C=100$. Hence, $$4B-100 =1015 \Rightarrow B=\frac{1115}{4}$$ Then we can find $A=\frac{1115}{2}$ and $C=\frac{715}{4}$. Hope it helps.

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If we lend them $\$100$, then we can give $B$ and $C$ the same amount of money, after which $C$ will give back the $\$100$ note.

Now, if we give $\$1$ to $B$ and $C$, $A$ will receive $\$2$. The total would be $\$4$.

OK, but we have $\$1115$ to distribute.

Just divide $1115$ by four, two parts to $A$, one part to $B$ and $C$. Don't forget to get back $\$100$ from $C$.

egreg
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  • Well thank you, man. Thank you. – MathX00 Dec 12 '16 at 16:17
  • @MathX00 You may find it instructve to translate that above into algebraic language. Doing so yields the following, which is the essentially same way that Rohan solved it.

    $$\begin{align}\rm
    \rm N &=,\rm \ A, +, B,\ \ +,\ \ \color{}C \ &=,\rm 2B +, B, +, \color{}{B!-!\color{#C00}{!100}}\ \iff \rm \color{#C00}{100}+N, &=,\rm 2B +, B, +, B\ &=,\rm 4B \end{align}$$

     – Bill Dubuque Dec 12 '16 at 17:17