Year 9 Interactive Maths - Second Edition

Problem Solving Unit

Problem 2.1  Concentration of the Solution

Problem 2.2  Number of Solutions

How many solutions to 7x + 3y = 93 are there for which x and y are positive integers?

Problem 2.3  Whole Numbers

Find five consecutive whole numbers that add up to 90.

Problem 2.4  Taxi Charge

Problem 2.5  The Age

When my mother was 43, I was 11.  Now she is twice as old as I am.  How old I am?

Problem 2.6  My Number

I am thinking of a number.  If I multiply it by 7 and subtract 8, I get the same number as if I had multiplied it by 6 and added 4.  What is my number?

Problem 2.7  Sound Together

b.  Foghorn P sounds every 26 seconds, and Foghorn Q sounds every 46 seconds.  They sound together at noon.  How many seconds later will they next sound together?

Problem 2.8  My Number

I am thinking of a number.  If I add a third, a sixth, and a ninth of it together, I get a total of 55.  What is my number?

Problem 2.9  Crossing a Bridge

Speed (or velocity) is the rate of change of distance with respect to time.  That is:

In symbolic form,

where     v denotes the velocity (or speed)
              d denotes the distance moved, and
              t denotes the time taken

Use the concept of speed to find the solution to the following problem: