### Brain Teasers

# Algebraic Sugar Cane

10 factories produce sugar cane. The second produced twice as much as the first. The third and fourth each produced 80 more than the first. The fifth produced twice as much as the second. The sixth produced 40 more than the fifth. The seventh and eighth each produced 40 less than the fifth. The ninth produced 80 more than the second. The tenth produced nothing due to drought in Australia. If the sum of the production equaled 11,700, what did the first factory produce?

### Hint

Use algebra. Eg / The first factory is X and the second is 2X.### Answer

500. First write down what each factory produced in relation to the first factory (whose production is X):1: X

2: 2X

3: X+80

4: X+80

5: 4X

6: 4X+40

7: 4X-40

8: 4X-40

9: 2X+80

10: 0X

Add them all up and set equal to 11,700 to get the equation:

23X + 200 = 11,700

Solution is: X = 500

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