Question

153 apples, 255 oranges, 357 pears are to be distributed to a group of children. Suppose each child in the group receives an equal number for each type of fruit.

a) Find the least possible number of children in the group

b) the maximum possible number of children in the group

c) the least possible number of apples, oranges and pears each child can receive

d) the maximum possible number of apples, oranges and pears each child can receive.​

Answer 1

a) 3 children

b) 51 children

c) 3 apples, 5 oranges and 7 pears

d) 51 apples, 85 oranges and 119 pears

Explanation:

lnc - Least possible number of children in group

mnc - maximum possible number of children in group

a - Apples

o - Oranges

p - Pears

a = 153

o = 255

p = 357

a)

To solve this, find the highest divisor for the apples, oranges and pears.

`a = (153)/(51)`

`a = 3`

`o = (255)/(85)`

`o = 3`

`p = (357)/(119)`

`p = 3`

In order for each child to get 51 apples, 85 oranges and 119 pears, there would need to be a minimum of 3 children in the group.

`lnc \: = 3`

b)

To solve this, find the lowest divisor for the apples, oranges and pears.

`a = (153)/(3)`

`a = 51`

`o = (255)/(5)`

`o = 51`

`p = (357)/(7)`

`p = 51`

In order for each child to get 3 apples, 5 oranges and 7 pears, there would need to be a maximum of 51 children in the group.

`mnc = 51`

c)

In a group of 51, each child will get:

- 3 apples

- 5 oranges

- 7 pears

d)

In a group of 3, each child will get

- 51 apples

- 85 oranges

- 119 pears

Answer 2

Below in bold.

Explanation:

a) we need the grestest common factor of theses values

153 = 3 * 3 * 17

255 = 3 * 5*17

357 = 3 * 7 * 17

The GCF = 3 * 17 = 51.

a) the least possible number of children is 3.

b) The maximum number is 51 ( as 51 is the GCF of the given values).

c) the least possible number of fruits is when b) occurs, that is:

153/51, 255/51 and 357/51

= 3 apples , 5 oranges and 7 pears.

d) the maximum number of fruits is :

153/3, 255/3 and 357/3

= 51 apples , 85 oranges and 119 pears.