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.
