Question

Callie bought a bag of dried fruit: cherries, pears, and apples.In the bag,1/4 of the dried fruit is cherries and 2/3 of the remainder is pears.There are 48 pear pieces. How many pieces of fruit are apples.

Answer 1

To find out the number of apple pieces, we determined the total number of pieces in the fruit bag using the information that 2/3 of the remainder after removing cherries were pears (48 pieces), resulting in 24 apple pieces.

Step-by-step explanation:

Callie bought a bag of dried fruit with cherries, pears, and apples. 1/4 of the dried fruit is cherries, and 2/3 of the remainder is pears. Given there are 48 pear pieces, we need to calculate how many pieces of fruit are apples.

Firstly, let's find the total number of pear pieces representing 2/3 of the remaining fruit after taking out the cherries:

48 pear pieces = 2/3 of the remainder

So, the remainder is:

48 / (2/3) = 48 * (3/2) = 72 pieces

Now, the total number of fruit pieces in the bag is:

(72 pieces / (3/4)) = 96 pieces

Since 1/4 of the pieces are cherries, we have:

96 pieces * (1/4) = 24 cherries

The number of apple pieces will then be the total minus cherries and pears:

Apples = 96 - 24 (cherries) - 48 (pears) = 24 apples

Answer 2

There 24 pieces of Apples in the bag of dry fruit.

Step-by-step explanation:

Let the total number of dried fruit bought be 'x'.

Given:

1/4 of the dried fruit is cherries.

Hence Number of cherries =
`(1)/(4)x`

Also Given:

2/3 of the remainder is pears.

Hence we can say Number of pears is equal to 2/3 times Total number of dried fruit minus Number of cherries.

Framing the equation we get;

Number of Pears =
`(2)/(3) (x-(1)/(4)x) = (2)/(3) x- (2)/(12)x= (2)/(3) x- (1)/(6)x`

But Given:

Number of Pears = 48

Substituting the values we get;

`(2)/(3) x- (1)/(6)x= 48\\`

By taking L.C.M we get;

`(2*2)/(3* 2) x- (1*1)/(6*1)x= 48\\\\(4)/(6) x- (1)/(6)x= 48\\\\(4x-x)/(6)=48\\\\(3x)/(6)=48\\\\(x)/(2)=48\\\\x= 48*2= 96`

Hence Total Number of Dry fruit = 96 pieces.

Number of cherries =
`(1)/(4)x=(1)/(4) * 96 = 24`

Now We need to find the Number of Pieces of Apples.

We know that Total Number of Pieces of dried fruit is equal to sum of Number of cherries and Number of Pears and Number of Apples.

Framing Equation we get

Number of Pieces of Apples= Total Number of Pieces of dried fruit - Number of cherries - Number of Pears = 96-48-24 =24 pieces

Hence There 24 pieces of Apples in the bag of dry fruit.