Answer: The ratio is 23:5
Step-by-step explanation:
The prices are x:y
This means that if phone 1 cost x dollars, phone 2 cost y dollars.
then we have:
(x + 20):(y + 20) = 5:2
this means that the ratios are comparable, so we have:
(x + 20)/(y + 20) = 5/2
we also have that:
(x - 5):(y - 5) = 5:1
so we again can have:
(x - 5)/(y - 5) = 5
So we have a system of equations:
(x + 20) = (5/2)(y + 20)
(x - 5) = 5(y - 5)
In order to solve it, we can isolate one of the variables in one of the equations and then replace it in the other equation.
(x - 5) = 5(y - 5) = 5y - 25
x = 5y - 25 + 5 = 5y - 20
now we can replace it in the first equation:
(x + 20) = (5/2)(y + 20)
(5y -20 + 20) = (5/2)(y + 20)
and solve it for y.
(5y) = (5/2)(y + 20) = (5/2)y + 50
5y - (5/2)y = 50
(5/2)y = 50
y = 50(2/5) = 100/5 = 20
y = 20, then:
x = 5y - 20 = 5*50 - 20 = 250 - 20 = 230
the ratio is 230:50
For writting it down, we can divide both numbers by a common factor, for example, 10:
230:50 = 23:5
23 and 5 are prime numbers, so we can not simplify it any more.
