CindySchweinsberg
19

# 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.

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.