Let's denote the number of Kate's friends as F and the total number of stickers she has as S.

From the first condition, we know that if she gives each friend 70 stickers, she will have 30 stickers left. This can be written as:

S - 70F = 30

From the second condition, we know that if she gives each friend 80 stickers, she will be short of 60 stickers. This means she needs 60 more stickers to give each friend 80. This can be written as:

S - 80F = -60

Now we have a system of two equations, and we can solve it step by step.

First, let's subtract the second equation from the first one:

(S - 70F) - (S - 80F) = 30 - (-60)

This simplifies to:

10F = 90

So, F = 90 / 10 = 9

So, Kate has 9 friends.

Question

Let's denote the number of Kate's friends as F and the total number of stickers she has as S.

From the first condition, we know that if she gives each friend 70 stickers, she will have 30 stickers left. This can be written as:

S - 70F = 30

From the second condition, we know that if she gives each friend 80 stickers, she will be short of 60 stickers. This means she needs 60 more stickers to give each friend 80. This can be written as:

S - 80F = -60

Now we have a system of two equations, and we can solve it step by step.

First, let's subtract the second equation from the first one:

(S - 70F) - (S - 80F) = 30 - (-60)

This simplifies to:

10F = 90

So, F = 90 / 10 = 9

So, Kate has 9 friends.

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