How to find the value of one unit
Hi Bubu. The value of one sticker? I'm not sure what you mean. If you'd like to solve the exercise using arithmetic, then here's one way. It begins with some analysis.
We're told Geraldine had 1/3 as many stickers as Kim (before they each gave away 18 stickers). That means Kim started with 3 times as many stickers as Geraldine did:
3 × Geraldine's beginning stickers = Kim's beginning stickers
Therefore, at the beginning, Kim's stickers were a multiple of 3.
Let's do the same analysis for the final sticker numbers. We're told that Geraldine had 1/5 as many stickers as Kim. That's the same as saying:
5 × Geraldine's final stickers = Kim's final stickers
Therefore, at the end, Kim's stickers were a multiple of 5.
Geraldine had to begin with at least 18 stickers. For an example, let's see how many stickers Kim had at the beginning and end, if Geraldine began with 18.
3 × 18 = 54
54 - 18 = 36
In that example, Kim's beginning stickers are a multiple of 3, but the final stickers are not a multiple of 5.
We list multiples of 3 greater than 54, and next to those we list the differences after subtracting 18. We're looking for differences that are multiples of 5. Multiples of 5 always end in 5 or 0.
57, 39
60, 42
63, 45
66, 48
69, 51
72, 54
75, 57
78, 60
60 is the first multiple of 5. Let's check that case.
Geraldine began with 1/3 of Kim's stickers and then gave 18 away.
78 ÷ 3 = 26
26 - 18 = 8
Geraldine ended with 8. Kim ended with 60. Therefore, 60 needs to be 5 times larger than 8.
5 × 8 ≠ 60
The check using 60 failed. We continue the list, until we get another multiple of 5 to check.
We only need to check a few more cases, to find the one that works.
?