Question

On Monday morning Mr. Smith had a certain amount of money that he planned to spend during the week. On each subsequent morning, he had one fourth the amount of the previous morning. On Saturday morning, $5$ days later, he had 1$.HowmanydollarsdidMr.SmithoriginallystartwithonMondaymorning?(Disregardthe$ sign when gridding your answer.)

• A. $1024$
• B. $2025$
• C. $1520$
• D. $1890$

Answer 1

The correct option is A $1024$

Lets denote the certain amount of money he had on Monday as $x$
Monday = $x$
Tuesday = $\frac{x}{4}$ (one-fourth of previous morning)
Wednesday = $\frac{x}{16}$
Thursday = $\frac{x}{64}$
Friday = $\frac{x}{256}$
Saturday = 1$
Now one-fourth of Friday morning's amount = $\frac{1}{4}\frac{x}{256}=\frac{x}{1024}=$1$
If $1=\frac{x}{1024}$. Then $x=1024$
Therefore, On Monday morning, he had 1024.$