Question

The prices of two radios are in the ratio x:y

Answer 1

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.

Answer 2

Answer:

$\frac{80}{20}=\frac{4}{1}$

Step-by-step explanation:

Let's call $x$ and $y$ the prices. Initially, the ratio of the prices is

$\frac{x}{y}$

So, if the prices are both increased by 20, the ratio becomes 5:2, that can expressed as follows

$\frac{x+20}{y+20}=\frac{5}{2}$

Then, if the prices are both reduced by 5, the ratio becomes 5:1, that is

$\frac{x-5}{y-5}=\frac{5}{1}$

To solve this problem, we just need to substitute one equation into the other one, let's isolate $x$ from the first proportion

$\frac{x+20}{y+20}=\frac{5}{2}\\x+20=\frac{5(y+20)}{2}\\ x=\frac{5y+100}{2}-20\\x=\frac{5y+100-40}{2} \\x=\frac{5y+60}{2}$

Now, we substitute $x$ into the second proportion and solve for $y$

$\frac{x-5}{y-5}=\frac{5}{1}\\x-5=5(y-5)\\\frac{5y+60}{2}-5=5y-25\\ \frac{5y+60-10}{2}=5y-25\\ 5y+50=10y-50\\50+50=10y-5y\\5y=100\\y=\frac{100}{5}=20$

Then, we use this value to find the other one, by replacing it into the result of the first propotion

$x=\frac{5y+60}{2}\\x=\frac{5(20)+60}{2}=\frac{100+60}{2}=\frac{160}{2}\\ x=80$

This means the ratio  $x:y$ is

$\frac{80}{20}$

But, we can reduce it by simplifying both parts of the ratio

$\frac{80}{20}=\frac{4}{1}$

Therefore, the ratio $x:y$ in its lowest terms is

$\frac{80}{20}=\frac{4}{1}$