Question by Lê Quốc Trần Anh - Discuss with MathYouLike

Lê Quốc Trần Anh Coordinator

03/01/2018 at 17:03

A two-year study was just completed. The project began with 40 participants and ended with 90 participants. After the first year, P participants were in the study. If the percent increase of the number of participants was the same for both years, what is the value of P?

List of answers

07NK-6789 Coordinator 03/01/2018 at 19:10

Call the percent increase is x (%)

Because the number of participants increase each year study.

We have equation :

\(\left\{{}\begin{matrix}P=40+40\cdot x\%\\P+P\cdot x\%=90\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}P=40+40\cdot x\%\\40+40\cdot x\%+\left(40+40\cdot x\%\right)\cdot x\%=90\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}P=40+40\cdot x\%\\x\%=50\%\end{matrix}\right.\)

So \(P=40+40\cdot50\%=60\)

Answer P = 60.
Lê Quốc Trần Anh selected this answer.
Asuna Yuuki 03/01/2018 at 20:04

Call the percent increase is x (%)

Because the number of participants increase each year study.

We have equation :

${\begin{matrix} P = 40 + 40 \cdot x % \\ P + P \cdot x % = 90 \end{matrix}$

$\Leftrightarrow {\begin{matrix} P = 40 + 40 \cdot x % \\ 40 + 40 \cdot x % + (40 + 40 \cdot x %) \cdot x % = 90 \end{matrix}$

$\Rightarrow {\begin{matrix} P = 40 + 40 \cdot x % \\ x % = 50 % \end{matrix}$

So $P = 40 + 40 \cdot 50 % = 60$

Answer P = 60
FA Liên Quân Garena 08/01/2018 at 21:48

Call the percent increase is x (%)

Because the number of participants increase each year study.

We have equation :

{P=40+40⋅x%P+P⋅x%=90

⇔{P=40+40⋅x%40+40⋅x%+(40+40⋅x%)⋅x%=90

⇒{P=40+40⋅x%x%=50%

So P=40+40⋅50%=60

Answer P = 60.

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