Question

Regina brought 8 7/8 pound of fruit for her family . She brought 3 1/2 pound of oranges and 2 3/4 pound of peaches and some apples .How many pounds of apples did Regina buy?

Answer 1

Regina has bought
`2(5)/(8)\ pounds` of apples.

Explanation:

Given:

Amount of fruit brought =
`8(7)/(8)\ pounds`

Now given number is in mixed fraction we will convert into improper fraction.

To convert a mixed fraction to an improper fraction, we will Multiply the whole number part by the fraction's denominator. Add that to the numerator,Then write the result on top of the denominator.

So we can say that;

`8(7)/(8)\ pounds` can be Rewritten as
`(71)/(8)\ pounds`

Amount of fruit brought =
`(71)/(8)\ pounds`

Also given:

Amount of oranges bought =
`3\frac12\ pounds`

`3\frac12\ pounds` can be Rewritten as
`(7)/(2)\ pounds`

Amount of oranges bought =
`(7)/(2)\ pounds`

Amount of peaches bought =
`2 \frac34\ pounds`

`2 \frac34\ pounds` can be Rewritten as
`(11)/(4)\ pounds`

Amount of peaches bought =
`(11)/(4)\ pounds`

We need to find amount of apples bought by Regina.

Solution:

Let the amount of apples bought be 'x'

Now we know that;

Amount of fruit brought is equal to sum of Amount of oranges bought and Amount of peaches bought amount of apples.

framing in equation form we get;

`(71)/(8)=(7)/(2)+(11)/(4)+x\\\\x=(71)/(8)-(7)/(2)-(11)/(4)`

Now we will make the denominator common using LCM we get.

`x=(71* 1)/(8* 1)-(7*4)/(2*4)-(11*2)/(4*2)\\\\x=(71)/(8)-(28)/(8)-(22)/(8)`

Now denominators are same so we will solve the numerator.

`x=(71-28-22)/(8)\\\\x=(21)/(8)\ pounds`

Now
`(21)/(8)\ pounds` can be Rewritten as
`2(5)/(8)\ pounds`

Hence Regina has bought
`2(5)/(8)\ pounds` of apples.