Question

the ratio of the number of apples to the number of oranges is 4:6. The ratio of the number of oranges to the number of pears is 8:1. How many apples, Oranges and pears are there if there are 172 fruits.

Answer 1

The answer is 64 apples, 96 oranges, and 12 pears.

Let's represent the fruit as following:
a - the number of apples,
o - the number of oranges,
p - the number of pears.

$a:o=4:6$
⇒ $\frac{a}{o}= \frac{4}{6}$
⇒ $a= \frac{4}{6}o$

$o:p=8:1$
⇒ $\frac{o}{p}= \frac{8}{1}$
⇒ $o= 8p$

Therefore:
$a= \frac{4}{6}*8p =16/3p$

Now, if $a+o+p=172$, then:
$\frac{16}{3}p +8p+p=172$
$\frac{16}{3}p +9p172$

Since $9= \frac{9}{1} = \frac{27}{3}$, 9p can be expressed as 27/3p:
$\frac{16}{3}p+ \frac{27}{3}p=172$
$\frac{43}{3}p =172$
⇒ $p =172* \frac{3}{43}$
⇒ p = 12
There are 12 pears.

Since o = 8p, o = 96:
o = 8 × 12 = 96
There are 96 oranges.

Since $a= \frac{16}{3}p$, a = 64:
$a= \frac{16}{3} *12=16*4=64$
There are 64 apples.

Therefore, there are 64 apples, 96 oranges, and 12 pears.