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

Answer:

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 = $\frac{1}{4}x$

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 = $\frac{2}{3} (x-\frac{1}{4}x) = \frac{2}{3} x- \frac{2}{12}x= \frac{2}{3} x- \frac{1}{6}x$

But Given:

Number of Pears = 48

Substituting the values we get;

$\frac{2}{3} x- \frac{1}{6}x= 48$

By taking L.C.M we get;

$\frac{2\times2}{3\times 2} x- \frac{1\times1}{6\times1}x= 48\\\\\frac{4}{6} x- \frac{1}{6}x= 48\\\\\frac{4x-x}{6}=48\\\\\frac{3x}{6}=48\\\\\frac{x}{2}=48\\\\x= 48\times2= 96$

Hence Total Number of Dry fruit = 96 pieces.

Number of cherries = $\frac{1}{4}x=\frac{1}{4} \times 96 = 24$

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.