How to find the value of one unit

Bubu

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How to find the value of one unit
 

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Your question about the value of one unit (when the problem doesn't involve values or units) suggests to me that you are not using algebra as most of us would here (presumably because you haven't learned algebra yet, thus the category you put this into).

It will help a lot if you show us enough work (or at least another example you were able to solve) so we can be sure what method you are trying to use. Is it perhaps a visual method where you make strips representing "units" divided into fractions?
 
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.

?
 
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If you have been Introduced to algebra, here is how you would use algebra for this problem.

Let "K" be the number of stickers Kim has and let "G" be the number of stickers Geraldine has.

"Geraldine hae 1/3 as many stickers as Kim had." So G= (1/3)K which (multiply both sides of the equation by 3) is the same as K= 3G.

"After they each gave away 18 stickers" so now Kim has K-18 stickers and Geraldine has G- 18 stickers.

"Geraldine then has 1/5 as many stickers as Kim." So G- 18= (1/5)(K- 18) which (multiply both sides of the equation by 5) is the same as K-18= 5(G- 18)= 5G- 5(18)= 5G- 90. Adding 18 to both sides of the equation, K= 5G- 72.

So we have both K= 3G and K= 5G- 72. Since both 3G and 5G- 72 are equal to K, they are equal to each other: 3G= 5G- 72. Subtract 5G from both sides: -2G= -72. Divide both sides by -2: G= 36.

So Geraldine originally had 36 stickers. Since "Geraldine had 1/3 as many stickers as Kim", Kim had 3 times as may stickers as Geraldine so Kim had 3(36)= 108 stickers.

Geraldine had 36 stickers and Kim had 108 stickers.

Check: Geraldine had 36/108= 1/3 as many stickers as Kim. After each gave away 18 stickers, Geraldine has 36- 18= 18 stickers and Kim had 108- 18= 90 stickers. Geraldine now had 18/90= 1/5 as many stickers as Kim.
 
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