Sarin participates in school anniversary event part 7(math question)

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Read posting Sarin participates in school anniversary event part 1 for school anniversary.

Upper primary school mathematics question UPQ96

Sarin was given a box of clips to use at the anniversary event. There were twice as many blue clips as yellow clips in the box. After used 66 blue clips and 8 yellow clips, there were thrice as many yellow clips as blue clips left in the box. How many clips were there in the box at first?

Solution:

Draw a model for blue clips and yellow clips.

Compare the clips before and after used.

Define 1U as 1 unit of clips after used.

Per the model,

                        5U = 50

                        1U = 10

                        Number of blue clips in the box at first = 10 + 66 = 76

                        Number of yellow clips in the box at first = 3 × 10 + 8 = 38

                        Number of clips in the box at first = 76 + 38 = 114

Alternative solution:

 

                        B = Y

                        1U = B + B – 66 = 2B – 66 = 2Y – 66

                        1U = (Y – 8)/3

                        2Y – 66 = (Y – 8)/3

                        6Y – 198 = Y – 8

                        5Y = 190

                        Y = 38

                        Number of clips in box at first = 3 × 38 = 114

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