In a basket are 80 bananas, oranges and apples. The number of oranges is 5 more than 1/3 the number of apples.The number of bananas is 1less than 1/4 the number of apples. How many bananas, apples...

In a basket are 80 bananas, oranges and apples. The number of oranges is 5 more than 1/3 the number of apples.

The number of bananas is 1less than 1/4 the number of apples. How many bananas, apples and oranges are in the basket?

Asked on by pengui

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The total number of fruits in the basket is 80. Let the number of bananas be B, the number of oranges O and the number of apples A.

The number of oranges is 5 more than (1/3) the number of apples.

This gives O = (1/3)*A + 5

The number of bananas is 1 less than (1/4) the number of apples

This gives B = (1/4)*A - 1

As the total number of fruits is 80

=> A + (1/3)*A + 5 + (1/4)*A - 1 = 80

=> A(1 + 1/3 + 1/4) = 76

=> A(19/12) = 76

=> A = 4*12 = 48

B = 11

O = 21

There are 48 apples, 11 bananas and 21 oranges in the basket.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Let the number of apples be x.

Let the number of oranges be y:

y = 5 + (1/3)*x (1)

Let the number of bananas be z:

z = (1/4)*x - 1 (2)

We know that the total number of fruits in the basket is of 80.

x + y + z = 80

We'll replace y and z by (1) and (2):

x + 5 + x/3 + x/4 - 1 = 80

12x + 4*12 + 4x + 3x = 12*80

19x = 960 - 48

19x = 912

x = 912/19

x = 48

y = 5 + 48/3

y = 5 + 16

y = 21

z = 48/4 - 1

z = 12 - 1

z = 11

Therefore, there are 11 bananas, 21 oranges and 48 apples in the basket.

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