# Question

a(ii) If you change two bags of pears for apples in Jermaine’s case, she would have bought exactly the same fruits as Karen.

Hence the difference is 2*(8-3)=10. Karen bought 10 more fruits.

b) Suppose the number of bags of oranges Linda bought is x,

Jermaine bought ‘a’ bags of apples , ‘b’ bags of pears;

5x=2+8a+3b

a+b=x

a+2=b

solve for a,b,x

would obtain x=6, a=2, b=4

The girls bought 3x=3*6=18 bags of fruits in total.

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Oh, i understand. We just need to find x which is the bags of oranges and multiply by 3 as every girl bought same number of bags. Thanks for ur help

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jermane’s apple and pear is ‘a’ and ‘p’ then what about karen

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Apples : Pears : Oranges

In 1 bag:        8        :  3       :       5

Jermaine :    Karen        : Linda

Same no. of bags                 a +   P    :     A      + p   :    or        , where P is p+2,  A is a+2 …[bags]

Rewrite ratio of bags        a + (p+2) :   (a+2) + p  :    or

Difference in no. of fruits      2×3     vs    2×8        vs     –      –> Karen has more and 10 more fruits#

J of apples :  J of pears : L of oranges

Ratio of bags                              u-1       :     u+1       :     let 2u

No. of fruits in each bag           8                   3                 5

Ratio of no. of fruits                (8u-8)  :   (3u+3)    :    10u

Equating:                                  (8u-8)  +   (3u+3)   =   10u -2  –> u=3

No. of bags = 2u bags x 3 girls = 18 bags#

Guess and check / Listing:

 Whofruit  (no. of fruits per bag) Japples (8) Jpear (3) Kapple (8) Kpear (3) Lorange (5) Jtotal #1) min. no. of bags 1 1+2=3 1+2 1 4 4 #1) no. of fruits 8 9 20 17  (diff=3) #2) next no. of bags 2 2+2=4 4 2 6 6 #2) no. of fruits 16 12 30 28  (diff=2) #3) next no. of bags 3 3+2=5 5 3 8 8 #3) no. of fruits 24 15 40 39  (diff=1)

No. of bags = 6 bags x 3 girls = 18 bags#

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(a)(i)
2 x 3 = 6 (pears)
2 x 8 = 16 (apples)
16 (K) > 6 (J)

(a)(ii)
16 – 6 = 10

(b)
In sets of 2, and its multiples, bags,
J : 6, 17, 28, …
K : 16, 27, 38, …
L : 10, 20, 30, …

2 x 3 x 3 = 18

Ans : (a)(i) Karen, (ii) 10 more fruits; (b) 18 bags.

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