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.

Answers

Answer 1

Answer: 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.

$a:o=4:6$
⇒ $(a)/(o)= (4)/(6)$
⇒ $a= (4)/(6)o$

$o:p=8:1$
⇒ $(o)/(p)= (8)/(1)$
⇒ $o= 8p$

Therefore:
$a= (4)/(6)*8p =16/3p$

Now, if $a+o+p=172$ , then:
$(16)/(3)p +8p+p=172$
$(16)/(3)p +9p172$

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

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

Since $a= (16)/(3)p$ , a = 64:
$a= (16)/(3) *12=16*4=64$
There are 64 apples.

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

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