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First, I calculated the prices:
£24 - 25 \% \times £24 = £18
£18 - \frac13 \times £18 = £12
£18 - 50\% \times £18 = £9
I used the following notation:
From the first store, with what it sold, I can write the following equation:
24x + 18y + 12z = 2010
which can be written as:
4x + 3y + 2z = 335 (eqn. 1)
If the store managed to sell all the CDs, I would have had:
24x + 18y + 30\times18 = 2370
or
4x + 3y = 305 (eqn. 2)
From the second store, I have the following information:
18x + 24y + 9u = 2010 (eqn. 3)
However, I know that:
x + y + 30 = x + y + u
So, u = 30
Now, I substitute u in equation (3):
18x + 24y + 9\times30 = 2010
or
3x + 4y = 290 (eqn. 4)
Now, I have a system of 3 equations ((1), (2), (4)) with 3 unknowns (x, y and z), so that I can calculate them all. First, I use equations (2) and (4).
From equation (2), I write x as a function of y:
x = (305 - 3y)/4 (eqn. 5)
Now, I substitute in equation (4), obtaining:
3 (305 - 3y)/4 + 4y = 290 (eqn. 6)
And from equation (6), I calculate y:
(16y - 9y + 915) = 1160
7y = 245
y = 35 (eqn. 7)
Now, I calculate x from equation (5):
x = 50 (eqn. 8)
And I calculate z from equation (1):
z = 15 (eqn. 9)
From 7, 8 and 9 we have:
50 CDs sold for £24
35 CDs sold for £18
15 CDs sold for £12.
A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?