Year 10 Interactive Maths - Second Edition

## Problem Solving Unit

### Problem 3.1  Triangular and Square Numbers

Triangular numbers can be modelled by dot figures as shown below.

Square numbers can be modelled by dot lattices as shown below.

a.  Write triangular numbers up to 100.
b.  Write square numbers up to 100.
c.  State the relation that exists between the square numbers and the triangular numbers.

### Problem 3.2  The Age

A's age equals B's age minus the cube root of C's age.  B's age equals C's age minus the square root of A's age, plus 24 years.  C's age equals the square root of A's age plus the cube root of B's age.  Find, by trial and error, the age of:

a. A in years
b. B in years
c. C in years

### Problem 3.3  Poppy

Poppy's dad paid her 50 cents for every problem she got right but penalised her 30 cents for any problem she got wrong.  After attempting 40 problems Poppy received only 80 cents. How many answers did she get right?

### Problem 3.4  Triangular Pyramid

1.  Apples are arranged so that they form the shape of an equilateral triangle. State the number of apples in the following diagrams.

2.  Apples are stacked in a triangular pyramid. Each layer of apples is in the shape of an equilateral triangle, and the layer at the top has one apple as shown in the following diagram.

State the number of apples in the:

a.  top layer
b.  second layer
c.  third layer
d.  fourth layer

3.  By observing the pattern, determine the number of apples in the:

a.  fifth layer
b.  sixth layer
c.  seventh layer
d.  eighth layer
e.  ninth layer
f.  tenth layer

4.  Determine the number of apples in a stack ten layers high.