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`
⇒
`(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.