Ken, Ahmad and Oliver had an average of 160 bookmarks. Ken had

36 bookmarks. The number of bookmarks Ahmad had was four times the total number of bookmarks Ken and Oliver had. How many more bookmarks did Ahmad have than Oliver?

1 answer

First, we need to find the total number of bookmarks that Ken, Ahmad, and Oliver had together. We know that:

Average = (Total sum of items) ÷ (Number of items)

So, we can write an equation for their average number of bookmarks:

160 = (Ken + Ahmad + Oliver) ÷ 3

Multiplying both sides by 3, we get:

480 = Ken + Ahmad + Oliver

We also know that Ken had 36 bookmarks, so we can substitute that into the equation:

480 = 36 + Ahmad + Oliver

Subtracting 36 from both sides, we get:

444 = Ahmad + Oliver

We also know that Ahmad had four times the total number of bookmarks that Ken and Oliver had. So, we can write another equation:

Ahmad = 4 × (Ken + Oliver)

Substituting Ken's value, we get:

Ahmad = 4 × (36 + Oliver)

Simplifying, we get:

Ahmad = 144 + 4Oliver

Now we can substitute this value back into our earlier equation:

444 = Ahmad + Oliver

444 = (144 + 4Oliver) + Oliver

300 = 5Oliver

Oliver = 60

So, Ahmad had:

Ahmad = 144 + 4Oliver

Ahmad = 144 + 4(60)

Ahmad = 384

Therefore, Ahmad had 384 bookmarks and Oliver had 60 bookmarks. Ahmad had 324 more bookmarks than Oliver.