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
