Question

The ratio of Martha's monthly pay to Kamila's monthly pay is 7:6 Both Martha and Khalid get an increase of £60 in their monthly pay. The ratio of Marta's monthly pay to Kamila's monthly pay after this increase is 15:13 Work out the monthly pay before the increase for Martha and for Kamila.​

Answer 1

• Martha: £840
• Kamilia: £720

Explanation:

You want to know the amounts Martha and Kamila were originally paid if an increase of £60 for each of them changed the ratio of their pay from 7:6 to 15:13.

Ratios

Let x be the multiplier of the original ratio. Then we have ...

(7x +60)/(6x +60) = 15/13

13(7x +60) = 15(6x +60)

x(7·13 -6·15) = 60(15 -13)

x = 60(15 -13)/(91 -90) = 120

The original pay amounts were ...

7 : 6 = 120(7) : 120(6) = 840 : 720

Martha was paid £840 per month, and Kamila was paid £720 per month.

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Additional comment

Writing the first ratio as 14:12, the second ratio of 15:13 represent an increase of 1 unit in each of the ratio numbers. Since the increase in pay was £60, this means each unit in either of these ratios is £60.

14:12 × £60 = £840:£720

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