Question

Auggie spent all of his money in 5 stores. In each store, he spent $1 more than one-half of what he had when he went in. How many dollars did Auggie have when he entered the first

Answer 1

Answer:

Total amount of Auggle when he entered the first = $62

Step-by-step explanation:

Let x be the total amount of Auggle when he entered the first.

Number of the store = 5

We need to find the total amount of Auggle when he entered the first.

Solution:

From the above statement he spent $1 more than one-half of total amount of Auggle when he entered the first.

⇒ $\frac{x}{2}+1$

⇒ $\frac{x+2}{2}$

So, when he leaves the first store

⇒ $x-\frac{x+2}{2}$

⇒ $\frac{2x-x-2}{2}$

⇒ $\frac{x-2}{2}$

When he go second store, he spends $\frac{x-2}{2\times 2}+1$

So, he has ⇒ $\frac{x-2}{4}-1$

⇒ $\frac{x-2-4}{4}$

⇒ $\frac{x-6}{4}$

Similarly for third store.

⇒ $\frac{x-6}{4\times 2} -1$

⇒ $\frac{x-6-8}{8}$

⇒ $\frac{x-14}{8}$

Similarly for fourth store.

⇒ $\frac{x-14}{8\times 2} -1$

⇒ $\frac{x-14-16}{16}$

⇒ $\frac{x-30}{16}$

Similarly for fifth store.

⇒ $\frac{x-30}{16\times 2} -1$

⇒ $\frac{x-30-32}{32}$

⇒ $\frac{x-62}{32}$

When he leaves the fifth store, he has $\frac{x-62}{32}=0$

⇒ $x-62=0$

$x = \ 62$

Therefore, Auggie have $62 when he entered the first store.