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The prices of two radios 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 ratio becomes 5:1
Express the ratio x:y in it's lowest terms.

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Kalahira
When the prices of two radios are increased by 20 we got the equation as 2x-5y=60. When the prices are reduced by 5 we got another equation as x-5y=60. By equating these two we will get zero for x and -twelve for y. the lowest terms of ratio is 0:-12.
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The concept of linear equation and ratios is used to solve for the price of radios. The price of two radios are [tex]x=\pounds 80[/tex] and [tex]y=\pounds 20[/tex].

Given information:

The ratio of prices of two radios is [tex]x:y[/tex].

If the price of both the radios is increased by [tex]\pounds20[/tex], the ratio of price would become 5:2.

The above condition can be written mathematically as,

[tex]\dfrac{x+20}{y+20}=\dfrac{5}{2}\\2x+40=5y+100\\2x-5y=60.........(1)[/tex]

If the prices are both reduced by [tex]\pounds 5[/tex], the ratio will become 5:1.

The above condition can be written mathematically as,

[tex]\dfrac{x-5}{y-5}=\dfrac{5}{1}\\x-5=5y-25\\x-5y=-20\\-x+5y=20.........(2)[/tex]

Add equation (1) and (2), to get the value of [tex]x[/tex] and [tex]y[/tex] as,

[tex]2x-x=60+20\\x=80[/tex]

Solve for [tex]y[/tex] as,

[tex]2x-5y=60\\2\times 80-5y=60\\5y=100\\y=20[/tex]

Therefore, the price of two radios is [tex]x=\pouns 80[/tex] and [tex]y=\pounds 20[/tex].

For more details, refer the link:

https://brainly.com/question/18836574