Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Homework Progress
31/43 Marks
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 its lowest terms.
Optional working
Answ
+
46%
​

Sagot :

sqdancefan

Answer:

  x : y = 4 : 1

Step-by-step explanation:

You want x:y, given adding 20 to both makes the ratio 5:2, and subtracting 5 from both makes the ratio 5:1.

Setup

The given relations tell us ...

  (x +20) : (y +20) = 5 : 2

  (x -5) : (y -5) = 5 : 1

Solution

Cross multiplying gives the equations ...

  2(x +20) = 5(y +20) . . . . . . . [eq1]

  (x -5) = 5(y -5) . . . . . . . . . . . . [eq2]

Solving [eq2] for x gives ...

  x = 5y -20

Substituting that into [eq1], we have ...

  2(5y -20 +20) = 5(y +20)

  10y = 5y +100

  5y = 100

  y = 20

  x = 5y -10 = 100 -20 = 80

Then x:y = 80:20 = 4:1.

The ratio x:y in lowest terms is 4:1.

__

Additional comment

When working with ratios, sometimes it works well to consider the difference of the numerator and denominator. Here, the difference when 20 is added is 5-2 = 3 "ratio units", which is 3/2 times the value y+20. The difference when 5 is subtracted is 5-1 = 4 "ratio units", which is 4 times the value y-5. Adding or subtracting the same number does not change the actual difference (x-y). This tells us ...

  (x -y) = 3/2(y+20) = 4(y-5)
  3y +60 = 8y -40
  100 = 5y
  20 = y
  x = y + 4(y-5) = 20 +4(15) = 80

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.