Number problems - calculating costs
Class 8RB are doing a charity bike ride.
The teacher of the class sponsors each pupil.
She says that if they take part in the race they will receive ÂŁ1 each.
To any student who cycles over 10 miles, the teacher will give an extra 15p for each mile they cycle in total.
The teacher recorded the number of miles cycled by the students:
2, 3, 7, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 14, 17, 18, 22, 24, 27, 30
How much money did the teacher give to the students to give to charity?
1. What do I have to do?
Read the question through twice. Highlight or underline the important pieces of information in the question.
2. What information do I need?
The highlighted words are the most important ones.
The most important parts of this question are:
- pupils each get ÂŁ1 each from their teacher for taking part
- anyone who cycles over 10 miles will be given 15 p per mile by the teacher in addition to the ÂŁ1 for taking part
The question asks for the total amount raised. The answer is money and not miles.
There are 20 items of data in the teacherâs list, so there are 20 students in the class, therefore the answer must be greater than ÂŁ20.
3. What information donât I need?
The name of the class and the fact it is a charity bike ride are not important when calculating the answer.
4. What maths can I do?
The list of data shows the number of miles each student cycled.
This provides the way into the question.
Step A
Check how many students took part in the bike ride by counting the numbers of pieces of data in the list.
2, 3, 7, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 14, 17, 18, 22, 24, 27, 30
20 students took part in the bike ride.
Step B
Work out how many miles the students, who did over 10 miles, cycled in total.
These are the miles that the teacher is paying 15 p per mile for.
\(11 + 12 + 13 + 14 + 14 + 14 + 17 + 18 + 22 + 24 + 27 + 30 = 216\:\text{miles}\)
Step C
Work out how much it costs the teacher for the 216 miles.
\(216 \times 15 = 3,240 \:\text{p}\)
Convert 3,240 pence into pounds and pence by dividing by 100.
\(3,240 \div 100 = \pounds32.40\)
Step D
The teacher agreed to pay each student ÂŁ1 for taking part so add on ÂŁ20 to the answer from step C.
\(32.40 + 20 = \pounds52.40\)
Therefore the teacher gives ÂŁ52.40 to the students for charity.
5. Is my solution correct?
It is important to check any calculations at the end.
Go through and check them, even if a calculator was used.
Does the answer make sense? ÂŁ52.40 seems a reasonable amount. For example, if you had forgotten to divide by 100, it would have been easy to put ÂŁ5,240, which seems wrong.
6. Have I completed everything?
The answer is supposed to be an amount of money.
It has got the correct number of decimal places and it seems reasonable.
Nothing else was asked for.