# Question

Hi I would appreciate it if I could get help with this question…

Gordon gave 1/3 of his sweets to Conrad. After that, Conrad gave Gordan 1/4 of what he had. In the end, Gordon had 64 sweets and Conrad had 72 sweets. How many sweets did Gordan have at first?

Thank you:)

Work backwards. Total sweets is unchanged (not used this concept, but can be a constant check)

 Gordon Conrad Total Final 64 72 (=3/4) 136 Conrad takes back his 1/4 64-24 96 (=4/4) 136 40 (=2/3) 96 136 Gordon takes back his 1/3 60 (=3/3) 96-20 136 Original 60 76# 136 checking: Gordon gives 1/3 60-20=40 76+20=96 136 Conrad gives 1/4 40+24=64 96-24=72 136

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This is a After Before question.

 Gordon Conrad Total After 64 72 (3u) Before 40  (2u) 96 (4u) Before 60 (3u) 76

73 ÷ 3 × 4 = 96

64 – 24 = 40

40 ÷ 2 × 3 = 60

96 – 20 = 76

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This is a After Before question.

 Gordon Conrad Total After 64 72 (3u) Before 40  (2u) 96 (4u) Before 60 (3u) 76

73 ÷ 3 × 4 = 96

64 – 24 = 40

40 ÷ 2 × 3 = 60

96 – 20 = 76

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Step 1: work backwards. Draw the model for 72 and 64.

step 2: since Conrad gave Gordon 1/4 he would have 3/4 left. So 3 units = 72

and 1 unit is 24.

Step 3: see red transfer. Gordon’s one unit of 24 has to be given back to Conrad.

step 4: since Conrad gave Gordon 1/3 of what he has, then he would have 2 units left .

2 units = 64-24 = 40.

so 1 unit = 20

and 3 units = 60.

gordan would have 72 + 4 = 76.

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