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?
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.
Let's solve step by step:
Step 1: Find the total number of bookmarks Ken, Ahmad, and Oliver had.
To find the total number of bookmarks, we can use the average and the number of bookmarks Ken had.
Let's assume the number of bookmarks Oliver had is "x".
Ken's bookmarks = 36
Total bookmarks = Average * Total people
Total bookmarks = 160 * 3 (for Ken, Ahmad, and Oliver)
Total bookmarks = 480
Step 2: Find the number of bookmarks Ahmad had.
According to the information provided, Ahmad had four times the total number of bookmarks Ken and Oliver had.
Ahmad's bookmarks = 4 * (Ken's bookmarks + Oliver's bookmarks)
Ahmad's bookmarks = 4 * (36 + x)
Ahmad's bookmarks = 4 * (36 + x)
Ahmad's bookmarks = 144 + 4x
Step 3: Find the number of bookmarks Oliver had.
We know that the average number of bookmarks is 160, so we can use this information to find the number of bookmarks Oliver had.
Total bookmarks = Average * Total people
480 = 160 * 3
480 = 480
We can substitute the value of the total bookmarks in terms of Oliver's bookmarks and solve the equation:
480 = 36 + x + 144 + 4x
Simplifying the equation:
480 = 36 + x + 144 + 4x
480 = 180 + 5x
480 - 180 = 5x
300 = 5x
x = 300/5
x = 60
So, Oliver had 60 bookmarks.
Step 4: Find the number of bookmarks Ahmad had.
Substituting the value of Oliver's bookmarks in Ahmad's bookmarks equation:
Ahmad's bookmarks = 144 + 4x
Ahmad's bookmarks = 144 + 4(60)
Ahmad's bookmarks = 144 + 240
Ahmad's bookmarks = 384
Step 5: Find the difference between Ahmad's and Oliver's bookmarks.
Difference = Ahmad's bookmarks - Oliver's bookmarks
Difference = 384 - 60
Difference = 324
Therefore, Ahmad had 324 more bookmarks than Oliver.