Bob initially had $30 , and correct option is A.
Step-by-step explanation:
We have , Bob spends 1/3 of his money bowling and loses half of the remainder. He has $10 left. We need to find how much did Bob have to start with . Let's start step by step solving questions!
Bob spends 1/3 of his money bowling
Let's assume that Bob had x rs money , so he spent 1/3 of x on bowling i.e. x/3.
Bob loses half of the remainder
Out of rs x he had , he spent x/3 in bowling so left is ( x - x/3 = [tex]\frac{2x}{3}[/tex] ) . And , he lost half of this i.e. [tex]\frac{2x}{3(2)} = \frac{x}{3}[/tex].
He has $10 left
He's now left with $10 . Now, total money spent = Total money he had i.e.
[tex]\frac{x}{3} + \frac{x}{3} + 10 = x[/tex]
⇒ [tex]\frac{x}{3} + \frac{x}{3} + 10 = x[/tex]
⇒ [tex]\frac{2x}{3} + 10 = x[/tex]
⇒ [tex]10 = \frac{x}{3}[/tex]
⇒ [tex]x = 30[/tex]
Therefore, Bob initially had $30 , and correct option is A.
