Multiple choice

Out of £20,000, Grace invested some amount at an interest of 6% and the remaining at 7%. If she earned £1280 interest, how much money did she invest at each rate separately?

  1. x = £8000, y = £18000

  2. x = £12000, y = £7000

  3. x = £9000, y = £15000

  4. x = £12000, y = £8000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be amount at 6%, y at 7%. x + y = 20000. 0.06x + 0.07y = 1280. 6x + 7y = 128000. 6x + 6y = 120000. y = 8000. x = 12000.

AI explanation

Setting up the system of equations based on the total investment and the total interest, we have x + y = 20000 and 0.06x + 0.07y = 1280. Multiplying the first equation by 0.06 gives 0.06x + 0.06y = 1200. Subtracting this from the interest equation yields 0.01y = 80, so y equals 8000. Substituting y back into the first equation gives x = 12000, confirming investments of £12000 at 6% and £8000 at 7%.

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