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When a
problem involves two unknowns we need to form two separate
equations from the given information. We will look at how
these problems are actually solved in the next section.
| e.g.
Prepare 2 simultaneous equations to find two numbers x
and y such that their sum is 24 and their difference
is 6. |
First,
let the larger of the two numbers be x.
The sum is x + y and the difference is x - y.
The two equations can therefore be expressed as 
| e.g.
500 tickets were sold for a rock and roll concert. Some
cost £5 and some cost £8. The cash received
for the dearer tickets was £100 more than for the
cheaper tickets. Prepare 2 simultaneous equations in order
to find the number of each kind of tickets that were sold. |
Let x
be the number of dearer tickets sold and y be the number
of cheaper tickets sold
500 tickets
were sold in total, so x + y = 500 (1)
The cash received for dearer tickets = 8x (in pounds)
The cash received for the cheaper tickets = 5y (in
pounds)
So from the information given we can also write 8x = 100
+ 5y (2)
The two
equations can therefore be expressed as 
| e.g.
At the present time a man is four times as old as his
son. Five years ago he was 7 times as old. Prepare 2 simultaneous
equations in order to find their present ages. |
Let x be the age of the man and y be the age
of the son at the current time.
At the present time we get the equation x = 4y. (1)
Five years ago the age of the man was x - 5 and the
age of the son was y - 5
So from the information given we can also write x - 5 =
7 (y - 5) (2)
Questions
7.1
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