Question

At a fruit stall, 2/7 of the fruits and another 14 fruits are apples. 1/3 of the remaining fruits and another 29 fruits are oranges. The rest of the fruits are mangoes. There are 65 mangoes at the fruit stall.

a) How many oranges are at the fruit stall?

b) Find the total number of fruits at the fruit stall.

(a)
65 + 29 = 94 (2/3 of the remaining)
(94/2) + 29 = 76 (oranges)

(b)
94 x (3/2) = 141 (3/3 of the remaining)
141 + 14 = 155 (5/7 of the fruits)
155 x (7/5) = 217

Ans : (a) 76 oranges; (b) 217 fruits.

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Draw  model (unfortunately cannot upload images)

From the sub model for remainder,

2u = 29 + 65

= 94

1u  = 94 ÷ 2

= 47

a) oranges at stall = 1u + 29

= 47 + 29

= 76 (ans)

Remainder = 3u

= 3 × 47

= 141

From the main model,

5 parts = 3u + 14

= 141 + 14

= 155

1 part = 155 ÷ 5

= 31

b) Total fruits = 7 parts

= 7 × 31

= 217 (ans)

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Amendment

2b – 29 = 65

2b = 65 + 29 = 94  (Addition error)

1b = 94 ÷ 2 = 47

a) 47 + 29 = 76 oranges

3b = 47 × 3 = 141

5a  – 14 = 141

5a = 141 + 14 = 155

1a = 155 ÷ 5 = 31

b)  7a = 7 × 31 = 217 fruits

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This is a Branching question.

 Apple orange mangoes total R1 2a + 14 5a – 14 7a R2 1b +29 2b – 29 3b

2b – 29 = 65

2b = 65 + 29 = 64

1b = 64 ÷ 2 = 32

a) 32 + 29 = 61 oranges

3b = 32 × 3 = 96

5a  – 14 = 96

5a = 96 + 14 = 110

1a = 110 ÷ 5 = 22

7a = 7 × 22 = 154 fruits

This is a Branching question.

Apple
orange
mangoes
total
R1
2a + 14

5a – 14
7a
R2

1b +29
2b – 29
3b
2b – 29 = 65
2b = 65 + 29 = 64
1b = 64 ÷ 2 = 32
a) 32 + 29 = 61 oranges
3b = 32 × 3 = 96
5a – 14 = 96
5a = 96 + 14 = 110
1a = 110 ÷ 5 = 22
7a = 7 × 22 = 154 fruits

At a fruit stall, 2/7 of the fruits and another 14 fruits are apples. 1/3 of the remaining fruits and another 29 fruits are oranges. The rest of the fruits are mangoes. There are 65 mangoes at the fruit stall.

154 x (2/7) = 44

44 + 14 = 58 (apples)

154 – 58 = 96

(96/3) + 29 = 61 (oranges)