3/16 of the fruits at a stall are pears. 1/4 of the remaining fruits are oranges. The rest are apples. If there are 585 apples, how many fru

3/16 of the fruits at a stall are pears. 1/4 of the remaining fruits are oranges. The rest are apples. If there are 585 apples, how many fruits are at the stall??

f = fruits    p = pears   o = oranges   a = apples

(1) $$p=f\cdot \frac3{16}$$

(2) $$o=(f-p)\frac14 \quad \text { or }\quad o = (f-f\frac3{16})\cdot \frac14 = f \frac{13}{16}\cdot \frac 14 = f\cdot\frac{13}{64}$$

(3) $$f = o+p+a$$

$$\small{\text{$
\begin{array}{rcl}
a &=& 585 \\
f &=& o+p+585 \\
f &=& o+p+585 \qquad | \qquad o = f\cdot\frac{13}{64} \qquad p=f\cdot \frac3{16}\\\\
f &=& f\cdot\frac{13}{64}+f\cdot \frac3{16}+585 \\\\
f - f\cdot\frac{13}{64}-f\cdot \frac3{16} &=& 585\\\\
f (1- \frac{13}{64}- \frac3{16}) &=& 585\\\\
f (\frac{64-13-3\cdot 4}{64}) &=& 585\\\\
f \cdot \frac{39}{64} &=& 585\\\\
f &=& 585 \cdot \frac{64}{39} \\\\
\mathbf{f} &\mathbf{=}& \mathbf{960}\\\\
\end{array}
$}} \\\\$$

At the stall are 960 fruits.

pears = 960 * (3/16) = 180

oranges = (960-180)/4 = 195

apples = 960 - 180 - 195 = 585 ( okay )

Hello MaiaMitchell !

Here my answer !

all fruits together:   x                             =>  1040

pears                 :   3/16 * x                  =>    195

oranges              :   1/4 * x                   =>    260

apples                :  585                          =>   585

$${\frac{{\mathtt{3}}}{{\mathtt{16}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{585}} = {\mathtt{x}}$$             |  * 16

3x + 4x  + 9360 = 16x

9360 = 9x     =>     x = 1040      ( all fruits )

Gruß radix !

Two different answers above!  Here's my version:

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