Auggie spent all his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?

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Multiple Choice

Auggie spent all his money in 5 stores. In each store, he spent Rs.4 more than one-half of what he had when he went in. How many rupees did Auggie have when he entered the first store?

Explanation:
The balance after each store is obtained by taking half of what you have and then subtracting 4. Since Auggie ends with nothing after the fifth store, work backward to find the starting amount. If the amount after the fifth store is 0, the amount just before that store must have been 2 × (0 + 4) = 8. Before the fourth store it would be 2 × (8 + 4) = 24. Before the third store: 2 × (24 + 4) = 56. Before the second store: 2 × (56 + 4) = 120. Before the first store: 2 × (120 + 4) = 248. So, Auggie had 248 rupees when he entered the first store.

The balance after each store is obtained by taking half of what you have and then subtracting 4. Since Auggie ends with nothing after the fifth store, work backward to find the starting amount.

If the amount after the fifth store is 0, the amount just before that store must have been 2 × (0 + 4) = 8. Before the fourth store it would be 2 × (8 + 4) = 24. Before the third store: 2 × (24 + 4) = 56. Before the second store: 2 × (56 + 4) = 120. Before the first store: 2 × (120 + 4) = 248.

So, Auggie had 248 rupees when he entered the first store.

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