Apple banana consumer problem math questions?

a consumer measures the utility u of possessing a quantity of x of apples and y of bananas by the formula u=u(x,y)=x^α y^(1-α) It is known that when the consumer budget for apples and bananas is £1 he will buy 1 apple and 2 bananas when they are equally priced. Use this information to find α? (answer α=1/3) (I am... show more a consumer measures the utility u of possessing a quantity of x of apples and y of bananas by the formula u=u(x,y)=x^α y^(1-α)
It is known that when the consumer budget for apples and bananas is £1 he will buy 1 apple and 2 bananas when they are equally priced. Use this information to find α? (answer α=1/3) (I am able to get this answer with Lagrange)

The price of apples falls to half that of bananas, with the price of bananas unchanged. How many apples and bananas will the consumer then buy for £10? (answer 20 of each)( I do not seem to be able to get this answer, if you would be able to help me, I would be really really thankful)
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