In a carton, 1/3 of the fruits were apples and the rest were pears and

Question

In a carton, 1/3 of the fruits were apples and the rest were pears and

kiwis. After Lynn gave away 2/3 of the apples, there were 12 apples left.

There were 5 times as many pears as kiwis.
(a) What fraction of the fruits did Lynn give away?
(b) How many pears were there in the carton?

Answer 1

Wow thanks a lot -_-

Answer 2

To solve this problem, let's break it down step by step:

Step 1: Determine the number of apples originally in the carton
Given that 1/3 of the fruits were apples and Lynn gave away 2/3 of the apples, we can set up the equation:
(1/3) * (1 - 2/3) * Total Fruits = 12 (remaining apples)

Simplifying the equation:
(1/3) * (1/3) * Total Fruits = 12
(1/9) * Total Fruits = 12

To isolate Total Fruits, we can multiply both sides by 9:
Total Fruits = 12 * 9 = 108

Therefore, there were originally 108 fruits in the carton.

Step 2: Determine the number of pears
Given that there were 5 times as many pears as kiwis, we can assume there were x kiwis in the carton. The number of pears would then be 5x.

So, the total number of fruits (108) can be expressed as:
Number of Apples + Number of Pears + Number of Kiwis = 108

Since 1/3 of the fruits were apples, we can represent the number of apples as:
Apples = (1/3) * 108 = 36

Given that Lynn gave away 2/3 of the apples, the remaining number of apples is:
Remaining Apples = 36 - (2/3) * 36 = 36 - 24 = 12

So, the equation becomes:
12 + Number of Pears + Number of Kiwis = 108

Given that the number of pears was 5 times the number of kiwis, we can represent it as:
Number of Pears = 5 * Number of Kiwis

Substituting this into the equation, we get:
12 + 5 * Number of Kiwis + Number of Kiwis = 108
12 + 6 * Number of Kiwis = 108

To isolate Number of Kiwis, we can subtract 12 from both sides:
6 * Number of Kiwis = 96

Finally, divide both sides by 6 to solve for Number of Kiwis:
Number of Kiwis = 96 / 6 = 16

Since there were 5 times as many pears as kiwis, the number of pears would be:
Number of Pears = 5 * 16 = 80

Therefore, the number of pears in the carton is 80.

(a) What fraction of the fruits did Lynn give away?
Lynn gave away 24 apples (36 - 12). The fraction of the fruits Lynn gave away would be:
Fraction = (Number of Apples Given Away) / (Total Fruits) = 24/108 = 2/9

Therefore, Lynn gave away 2/9 of the fruits.

(b) How many pears were there in the carton?
There were 80 pears in the carton.

Answer 3

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