The prices of two phones are in the ratio x : y.

when the prices are both increased by £20, the ratio becomes 5 : 2.
when the prices are both reduced by £5, the ratios becomes 5 : 1.

express the ratio x : y in its lowest form !

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.

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.