Question

This morning Allen had 2 more action figures than Barbara, and Barbara had 8 more action figures than Charlie. Allen have some of his action figures to Charlie, and now both Allen and Charlie have the same number of action figures. Barbara now has N more action figures than Charlie does. What is the value of N?

Answer 1

The value of N is 5.

Let x represent the number of action figures Allen has.

Let y represent the number of action figures Barbara has.

Let z represent the number of action figures Charlie has.

Generating the equations

Given that this morning Allen had 2 more action figures than Barbara, we have that x = y + 2 (1)

Also, Barbara had 8 more action figures than Charlie, we have that y = z + 8 (2)

Now, Allen have some of his action figures to Charlie, and now both Allen and Charlie have the same number of action figures.

Let p be the number of action figures Allen gave to charlie. So, Allen now has x - p action figures and Charlie now has z + p

Since now, both Allen and Charlie have the same number of action figures, we have that

x - p = z + p (3)

Barbara now has N more action figures than Charlie does.

So, y + N = z + p + 8 (4)

Solving the equations

Substituting (2) into (1), we have

x = y + 2

= z + 8 + 2

= z + 10

x = z + 10 (5)

The value of p

Substituting (5) into (3), we have

x - p = z + p

z + 10 - p = z + p

10 - p = p

10 = 2p

p = 10/2

p = 5

The value of N

Substituting (2) into (4), we have

y + N = z + p + 8

z + 8 + N = z + p + 8

N = p

Since p = 5, N = 5

So, the value of N is 5.

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