Barry buys 200 pieces of stationery for £76. Of the 200 pieces of stationery, x of them are rulers that cost 50p each and y of
them are pens that cost 20p each.
Find how many rulers Barry buys and how many pens he buys.

First, we take the first given information: 200 pieces = £76. Since the other unknowns are expressed in pence "p", we convert this amount to "p" = 76 x 100 = 7600p.

The information on "x" and "y" gives us 2 equations:

first:

x pieces + y pieces = 200 pieces (or x + y = 200)

placing "x" in terms of "y" gives us x = 200 - y

in terms of "y": y = 200 - x

50p(x) + 20p(y) = 7600p (or 50x + 20y = 7600)

solving for "x" gives:

x = (7600 - 20y) / 50

substituting y from our first equation gives:

x = (7600 - 20(200 - x)) / 50

x = (7600 - 4000 + 20x) / 50 (distribute - remember to distribute the negative sign)

x = (3600 + 20x) / 50 (simplify)

x = 360/5 + (2/5)x (subtract (2/5)x from both sides)

(3/5)x = 360/5

3x = 360

x = 120 (rulers bought)

substituting into our first equation:

y = 80 (pens bought)

check our solution using the second equation:

50x + 20y = 7600

50(120) + 20(80) = 7600

6000 + 1600 = 7600 (correct)

therefore:

x = 120 rulers Barry bought

y = 80 pens Barry bought