Question

Huixian needs 171 pens 63 pencils and 27 erasers into identical gift packs so that each item could equally distribiuted among tha bags find the number of each item in a gift bag

Answer 1

there will 7 pencils, 19 pens and 3 erasers in each bag of gift bag and total number of gifts bag will be 9.

Explanation:

Given:

Number of pens = 171 pens

Number of pencils = 63

Number of erasers = 27

We need to number of each items in the bags.

Solution:

First we will find the largest number of gift bags that can be packed.

To find the the largest number of gift bags that can be packed we need to find the greatest common factor of these numbers.

So we will List the prime factors for each number:

`171 = 3 * 3 * 19\\\\63 = 3 * 3 * 7\\\\27 = 3 * 3 * 3`

From above we can say that;

The greatest common factor of three numbers =
`3*3=9`

Hence There would 9 gifts bag to packed this item.

Now To find the Number of item in each bag we will divide number of items from the number of gifts bag.

framing in equation form we get;

Number of pencils in each =
`(63)/(9)=7\ pencils`

Number of pens in each bag =
`(171)/(9)=19\ pens`

Number of eraser in each bag =
`(27)/(9)=3\ erasers`

Hence there will 7 pencils, 19 pens and 3 erasers in each bag of gift bag and total number of gifts bag will be 9.