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 $\$1$. How many dollars did Mr. Smith originally start with on Monday morning?(Disregard the $\$$ sign when gridding your answer.)

Answer 1

Let $M$ be the initial amount of money Mr. Smith had

According to question,

Money on Monday $=M$

Money on Tuesday $=M/4$

Money on Wednesday $=M/16$

This forms a GP $M,\frac{M}{4},\frac{M}{16},\frac{M}{64},...$
On $5^{th}$ day (saturday) Money $=1$

$a{r}^5=1\left(M\right){\left(\frac{1}{4}\right)}^5=1M=4^5=2^{10}=1024$