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.
⇒ [tex]\frac{x}{2}+1[/tex]
⇒ [tex]\frac{x+2}{2}[/tex]
So, when he leaves the first store
⇒ [tex]x-\frac{x+2}{2}[/tex]
⇒ [tex]\frac{2x-x-2}{2}[/tex]
⇒ [tex]\frac{x-2}{2}[/tex]
When he go second store, he spends [tex]\frac{x-2}{2\times 2}+1[/tex]
So, he has ⇒ [tex]\frac{x-2}{4}-1[/tex]
⇒ [tex]\frac{x-2-4}{4}[/tex]
⇒ [tex]\frac{x-6}{4}[/tex]
Similarly for third store.
⇒ [tex]\frac{x-6}{4\times 2} -1[/tex]
⇒ [tex]\frac{x-6-8}{8}[/tex]
⇒ [tex]\frac{x-14}{8}[/tex]
Similarly for fourth store.
⇒ [tex]\frac{x-14}{8\times 2} -1[/tex]
⇒ [tex]\frac{x-14-16}{16}[/tex]
⇒ [tex]\frac{x-30}{16}[/tex]
Similarly for fifth store.
⇒ [tex]\frac{x-30}{16\times 2} -1[/tex]
⇒ [tex]\frac{x-30-32}{32}[/tex]
⇒ [tex]\frac{x-62}{32}[/tex]
When he leaves the fifth store, he has [tex]\frac{x-62}{32}=0[/tex]
⇒ [tex]x-62=0[/tex]
[tex]x = \$62[/tex]
Therefore, Auggie have $62 when he entered the first store.
