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Hakim and Aziz had some savings in the ratio 3 : 5. Hakim saved another $82 and Aziz spent $110. Both have the same amount of money now. How much do each of them have now?​

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3 votes

Answer: $370

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Step-by-step explanation:

Hakim and Aziz have savings in the ratio 3:5. This means that Hakim has 3x dollars while Aziz has 5x dollars. The x is some positive real number.

We're then told that Hakim saved another $82, which means it goes from 3x to 3x+82

At the same time, Aziz spent $110 which means the 5x decreases to 5x-110

At this point, the two people have the same amount of money. Set the expressions we found equal to one another and solve for x.

3x+82 = 5x-110

3x-5x = -110-82

-2x = -192

x = -192/(-2)

x = 96

Then use this x value to compute each expression like so

  • 3x+82 = 3*96+82 = 370
  • 5x-110 = 5*96-110 = 370

Both have $370 after Hakim saved that additional $82 and after Aziz spent that $110.

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Extra info:

If we rewind things a bit, Hakim would have 3*x = 3*96 = 288 dollars while Aziz would have 5x = 5*96 = 480 dollars. This is before any additional saving or spending.

Then note how the ratio 288:480 fully reduces to 3:5 after dividing both parts by the GCF 96.

User Mahmoud Adam
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