Question

Callie is starting a fruit basket business. The largest fruit basket will contain 30 pieces of fruit. Other baskets may contain fewer, but at least 12 piece of fruit. In every basket, 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas. What combinations of pieces of fruit represent all the possible fruit baskets Callie can make?

Find the common denominator, fractions, and combination of fruit for the numbers 30, 18, 24, and 12.

Answer 1

because i am in special ed

Explanation:

that means i know everthing beacuse im special

Answer 2

Common fractions =
`(1)/(2) ,(1)/(3) ,(1)/(6)=1`

Denominator = 6

combination of fruits in basket having 30 fruits :

`(1)/(2) *30=\text{15 apples}\\ \\(1)/(3) *30=\text{10 oranges}\\\\(1)/(6) *30=\text{5 bananas}\\`

Combination of fruits in basket having 18 fruits :

`(1)/(2) *18=\text{9 apples}\\ \\(1)/(3) *18=\text{6 oranges}\\\\(1)/(6) *18=\text{3 bananas}\\`

Combination of fruits in basket having 24 fruits :

`(1)/(2) *24=\text{12 apples}\\ \\(1)/(3) *24=\text{8 oranges}\\\\(1)/(6) *24=\text{4 bananas}\\`

Combination of fruits in basket having 12 fruits :

`(1)/(2) *12=\text{6 apples}\\ \\(1)/(3) *12=\text{4 oranges}\\\\(1)/(6) *12=\text{2 bananas}\\`

Explanation:

Let x be fruits in any basket

Since we are given that . In every basket, 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas.

Thus in basket having x fruits will have apples =
`(1)/(2) x`

And oranges =
`(1)/(3) x`

bananas =
`(1)/(6) x`

So, no matter how much fruits there in a basket the fraction of apples , oranges and bananas will remain same

So, Common fractions =
`(1)/(2) ,(1)/(3) ,(1)/(6)`

Denominator = 6

Now combination of fruits in basket having 30 fruits :

Since we are given that 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas.

`(1)/(2) *30=\text{15 apples}\\ \\(1)/(3) *30=\text{10 oranges}\\\\(1)/(6) *30=\text{5 bananas}\\`

Now combination of fruits in basket having 18 fruits :

Since we are given that 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas.

`(1)/(2) *18=\text{9 apples}\\ \\(1)/(3) *18=\text{6 oranges}\\\\(1)/(6) *18=\text{3 bananas}\\`

Now combination of fruits in basket having 24 fruits :

Since we are given that 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas.

`(1)/(2) *24=\text{12 apples}\\ \\(1)/(3) *24=\text{8 oranges}\\\\(1)/(6) *24=\text{4 bananas}\\`

Now combination of fruits in basket having 12 fruits :

Since we are given that 1/2 of the pieces of fruit must be apples, 1/3 must be oranges, and 1/6 must be bananas.

`(1)/(2) *12=\text{6 apples}\\ \\(1)/(3) *12=\text{4 oranges}\\\\(1)/(6) *12=\text{2 bananas}\\`