Question

4. Jim and Kirk are playing a card game where they trade chips. At the beginning of the game, Jim has four times as many chips as Kirk does. After Kirk wins the game, Jim gives Kirk 18 of his chips, at which point they now have the same number of chips. How many did Kirk have to begin with?

(a) If j represents the original number of chips Jim had and k represents the original number of chips that Kirk had, then write an equation that models the amount of chips they originally had. Explain your equation.

(b) The equation j k − = + 18 18models the scenario after Kirk wins the game. Explain why.

(c) Determine how many chips both Kirk and Jim started with.

Answer 1

(a)
`j = 4k`

(b)
`4k - 18 = 18 + k`

(c) Jim initially had 48; Kirk initially had 12

Explanation:

Given

`j = Jim`

`k=Krik`

Solving (a): An equation for the amount they originally had.

From the question, we understand that j is 4 times as many as k.

Mathematically, this is:

`j = 4 * k`

`j = 4k`

Solving (b): Equation after Kirk wins

Initially Kirk had k.

To get the new expression, we add 18 to k.

This gives: 18 + k

In the same vein, Jim's number of chirps will reduce by 18.

Initially, Jim had j chirps (or 4k chirps)

To get the new expression, we subtract 18 from j.

This gives: j - 18

So, the equation is:

`j - 18 = 18 +k`

Solving (c): Number of chirps they started with.

In (b), we have:

`j - 18 = 18 +k`

Substitute 4k for j

`4k - 18 = 18 + k`

Collect Like Terms

`4k - k = 18 + 18`

`3k = 36`

Divide both sides by 3

`k =12`

Substitute 12 for k in
`j = 4k`

`j = 4 * 12`

`j = 48`