Answer:
x= 260, y= 400
Step-by-step explanation:
Cost of mobile phone= x pounds
Cost of television= y pounds
When both prices are increased by £40,
cost of mobile phone= £(x +40)
cost of television= £(y +40)
[tex] \frac{x + 40}{y + 40} = \frac{15}{22} [/tex]
Cross multiply:
15(y +40)= 22(x +40)
Expand:
15y +600= 22x +880
-600 on both sides:
15y= 22x +280 -----(1)
When both prices decreased by £100,
cost of mobile phone= £(x -100)
cost of television= £(y -100)
[tex] \frac{x - 100}{y - 100} = \frac{8}{15} [/tex]
Cross multiply:
15(x -100)= 8(y -100)
15x -1500= 8y -800 (expand)
15x= 8y -800 +1500 (+1500 on both sides)
15x= 8y +700 (simplify)
[tex]x = \frac{8}{15} y + \frac{140}{3} [/tex] -----(2)
Subst. (2) into (1):
[tex]15y = 22( \frac{8}{15} y + \frac{140}{3} ) + 280[/tex]
Expand:
[tex]15y = \frac{176}{15} y + \frac{3080}{3} + 280 \\ 15y - \frac{176}{15} y = \frac{3080}{3} + 280 \\ \frac{49}{15} y = \frac{3920}{3} \\ y = \frac{3920}{3} \div \frac{49}{15} \\ y = 400[/tex]
Subst. y=400 into (2):
[tex] x= \frac{8}{15} (400) + \frac{140}{3} \\ x = \frac{640}{3} + \frac{140}{3} \\ x = \frac{780}{3} \\ x = 260[/tex]
