Year 10 Interactive Maths - Second Edition

Problem Solving Unit

Problem 2.1  The Party

Patricia bought one mango for each child invited to a party. However, one-third of the children didn't show up. If 15 boys came, and the surplus provided just one extra mango for each girl. Find how many:

a.  mangos were bought
b.  children came to the party
c.  girls came to the party

Problem 2.2  The Pupils

In a certain school, there are 1000 pupils in Year 9, Year 10 and Year 11. If there are 800 in Year 10 and Year 11, and 350 in Year 9 and Year 10, find how many pupils are in Year 10.

Problem 2.3  Father and Son

If a father is 43 years old and his son is 7 years old, in how many years will the father be three times as old as the son?

Problem 2.4  Weight of a Brick

On the following set of scales, one brick is balanced perfectly against 3 kilograms and half of a brick. How much does one brick weigh?

Problem 2.5  Selling Mangos

A grocer sent her three children to the market to sell mangos. The eldest had 40 mangos, the next eldest had 20, and the youngest had 10. The grocer instructed her children to sell their mangos at the same price, and not only that, but they must all bring home exactly the same amount of money, even though each child had a different number of mangos to sell. They are not allowed to trade or give away their mangos among themselves.

a.  Each child returned home with the same amount.  How did they manage to comply with the instructions?
b.  This problem has more than one answer. Explain.

Problem 2.6  The Final Age

A woman led 15% of her life in childhood, 7.5% of her life in youth, and was unmarried for a further 20% of her life. Three years after her marriage, a daughter was born who passed away three years before her mother at half her mother's final age.

What was the woman's final age?

Problem 2.7  Working Together

Ken takes 45 minutes to finish the gardening while Werner takes 30 minutes. How long should it take if they work together?

Problem 2.8  Marbles

A set of scales that is in balance has two pans. In one pan are five identical boxes full of marbles, as well as another box from which nine marbles have been taken. The second pan contains exactly 63 marbles (and 6 empty boxes). How many marbles are contained in a full box?

Problem 2.9  * Operation

Problem 2.10  Division by Zero

We know that:

This means division by 0 is undefined.

Problem 2.11  True or False

Which of the following statements are true?  Justify your answer by giving reasons.