four teenagers collected a total of £64 for charity. each teenager collected a whole number of pounds. the modal amount collected was £16. the range of the amounts collected was £2. work out how much each teenager collected?
please someone answer
Had they collected £16 each, the mode would have been £16 but the range would have been £0
So two of them must have been £2 apart
How about
£16, £16, £15, £17
Tutors come online at different times of the day, so you won't necessarily get immediate answers.
With 4 teens, at least two must have collected the modal amount 16 + 16.
64 - 32 = 32
With range of only 2, the remaining two must be one above and one below the mode.
To find out how much each teenager collected, we can use a logical approach and some basic arithmetic.
Given:
1. The total amount collected by four teenagers is £64.
2. Each teenager collected a whole number of pounds.
3. The modal amount collected was £16.
4. The range of the amounts collected was £2.
Let's break down the problem step by step:
Step 1: Find the range.
The range refers to the difference between the lowest and highest amounts collected. In this case, the range is £2.
Step 2: Deduce the highest and lowest amounts.
Since the range is £2, there are only two possible combinations for the highest and lowest amounts:
Combination 1 - Lowest: £14, Highest: £16
Combination 2 - Lowest: £15, Highest: £17
Step 3: Determine the total amount collected by the other two teenagers.
To find the remaining amounts collected by the other two teenagers, subtract the highest and lowest amounts from the total amount collected by all four teenagers (£64).
Combination 1:
Total amount collected by the other two teenagers = £64 - (£14 + £16) = £34
Combination 2:
Total amount collected by the other two teenagers = £64 - (£15 + £17) = £32
Step 4: Divide the total amount collected by the other two teenagers by two to get the individual amounts.
Since there are two remaining teenagers, we divide the total amount collected by the other two teenagers (from Step 3) by 2.
Combination 1:
Amount collected by each of the remaining teenagers in Combination 1 = £34 ÷ 2 = £17
Combination 2:
Amount collected by each of the remaining teenagers in Combination 2 = £32 ÷ 2 = £16
Therefore, there are two possible scenarios: In Combination 1, one teenager collected £14, one collected £16, and the remaining two teenagers each collected £17. In Combination 2, one teenager collected £15, one collected £17, and the remaining two teenagers each collected £16.