Tarun James Marcus and Yahya like to collect keychains and they have an average of 68 keychains. Tarun has 78 keychains. James has half as many keychains as Marcus. Yahya has 28 fewer keychains than the total number of keychains that James and Marcus have. How many keychains does each boy have

There are 4 people. They average 68, so the total key chains are 68 x 4 = 272.

Tarun has 78, so the other three people have a total of 272 - 78 = 194.

Let Marcus = X

James has half as many as Marcus, so he is 0.5X

Yahya is (x + 0.5x) - 28 = 1.5X-28

Now add them together to equal 194:

X + 0.5x + 1.5x - 28 = 194

Simplify:

3x - 28 = 194

Add 28 to each side:

3x = 222

Divide both sides by 3:

x = 222 / 3

x = 74

Marcus = x = 74 key chains.

James = 0.5x = 0.5 (74) = 37 key chains.

Yahya = 1.5x-28 = 1.5 (74) - 28 = 111-28 = 83 key chains.

Tarun = 78 key chains.

Check: 74 + 37 + 83 + 78 = 272 (matches the total above).