Question

A price is divided into 1:11. If the difference between the shares is £180, what is the total prize

Answer 1

Answer:

  £216

Step-by-step explanation:

The total prize will be the sum of the divisions of the prize. The difference of those divisions is given.

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divisions

Let P represent the value of the prize. The 1:11 ratio of the parts tells us there are 1 +11 = 12 total parts, and their ratio is P/12 : 11P/12. The sum of these divisions is the whole prize:

  P/12 +11P/12 = 12P/12 = P

difference

The difference of the two divisions of the prize is ...

  11P/12 -P/12 = £180

  10P = £2160 . . . . . . . . multiply by 12 and simplify

  P = £216 . . . . . . . . divide by 10

The total prize is £216.

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Additional comment

The divisions of the prize are

  £216/12 = £18  and  11×£18 = £198

The sum of those divisions is the total prize: £18 +198 = £216.

Answer 2

1:11 let’s say 1 = X
So: X:11X
11X - X = 10X = 180
X = 18 (180 : 10)
So total prize is: 18 X 11 = £198