16% of the pens in a stationery shop are red. The number of black pens is 3/4 the number of red pens. The number of green pens is 5/7 the to

pens percentage=100- (Red pens+Black pens+Green pens) =100-48 =52 (52% of all pens)=(48% of all pens)+180 →(4% of all pens)=180 So the total number of pens in the shop is 4500 pens.

Blue pens percentage=100- (Red pens+Black pens+Green pens)

                              =100-48

                              =52

(52% of all pens)=(48% of all pens)+180

→(4% of all pens)=180

So the total number of pens in the shop is 4500 pens.

16% of the pens in a stationery shop are red. The number of black pens is 3/4 the number of red pens. The number of green pens is 5/7 the total number if red and black pens. The rest of the pens in the shop are blue. The number of blue pens is 180 more than the number of red, black and green pens. Find the total number of pens in the shop

x are the number of the pens.

$$\\\small{
\begin{array}{rcl}
\textcolor[rgb]{150,0,0}{\text{red}} &=& 0,16x\\\\
\text{black}& =& \dfrac{3}{4}\textcolor[rgb]{150,0,0}{\text{red}} \\\\
\textcolor[rgb]{0,150,0}{green} &=& \dfrac{5}{7}( \textcolor[rgb]{150,0,0}{\text{red}} +\text{black} ) = \dfrac{5}{7}\textcolor[rgb]{150,0,0}{\text{red}} + \dfrac{5}{7}\cdot \dfrac{3}{4}\textcolor[rgb]{150,0,0}{\text{red}} = \dfrac{5}{4} \textcolor[rgb]{150,0,0}{\text{red}} \\\\
\textcolor[rgb]{0,0,150}{blue}& =& 180 + ( \textcolor[rgb]{150,0,0}{\text{red}} +\text{black} + \textcolor[rgb]{0,150,0}{green} )
= 180 + \textcolor[rgb]{150,0,0}{\text{red}} +\dfrac{3}{4}\textcolor[rgb]{150,0,0}{\text{red}}+\dfrac{5}{4} \textcolor[rgb]{150,0,0}{\text{red}} = 180 + 3\cdot \textcolor[rgb]{150,0,0}{\text{red}} \\\\\\
x &=& \textcolor[rgb]{150,0,0}{\text{red}} +\text{Black}
+\textcolor[rgb]{0,150,0}{green}+\textcolor[rgb]{0,0,150}{blue}\\\\
x &=& \textcolor[rgb]{150,0,0}{\text{red}}
+\dfrac{3}{4}\textcolor[rgb]{150,0,0}{\text{red}}
+\dfrac{5}{4} \textcolor[rgb]{150,0,0}{\text{red}}
+180 + 3\cdot \textcolor[rgb]{150,0,0}{\text{red}} \\\\
x &=& 6\cdot \textcolor[rgb]{150,0,0}{\text{red}} +180\\\\
x &=& 6\cdot 0.16x+180\\\\
x &=& 0.96x+180\\\\
x-0.96x &=& 180\\\\
0.04x &=& 180\\\\
x &=& \dfrac{180\cdot 100}{4}\\\\
\mathbf{x}& \mathbf{=}& \mathbf{4500}
\end{array}
}$$

The total number of pens in the shop is 4500

red = 720

black = 540

green = 900

blue = 2340