Mathland Election

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.

One or Both

Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

Weekly Problem 43 - 2013

Put Out the Flags

Stage: 3 Challenge Level:

Why do this problem?

This problem gives practice in calculating with percentages. It can be approached by trial and improvement but the equivalence between fractions and percentages is very useful.

Key questions

What fraction is $50$%? and $35$%?

What would be a sensible number to try first?

Do you think they will not have a whole number of flags?

Tim could have $100$ flags but could he have less than $100$ flags?

If $50$% of Tim's flags are blue, what does this tell you about the number of flags Tim must have?

As $35$% of Tim'??s flags are red, what does this tell you about the number of flags Tim must have?

Possible extension

Learners could devise and solve a second part to the question, similar to that one in the problem.

Possible support

Suggest working with counters or drawing the flags starting with a suitable arbitrary number and working by trial and improvement.

Diophantine equations. Calculating with percentages. Mixed fractions, decimals and percentages. smartphone. Spreadsheets. Percentages. Money.

You may also like