A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is 20% more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671 . How many shoppers were at the mall on the first day? Round your final answer to the nearest integer. ◻ shoppers

Question

A new shopping mall is gaining in popularity. Every day since it opened, the number of shoppers is  20% more than the number of shoppers the day before. The total number of shoppers over the first 4 days is 671 . How many shoppers were at the mall on the first day? Round your final answer to the nearest integer.  ◻ shoppers

Bytelearn · Accepted Answer

Denote Shoppers: Let's denote the number of shoppers on the first day as $ S $. According to the problem, each day the number of shoppers is 20% more than the previous day. This means that on the second day, there are $ S \times 1.20 $ shoppers, on the third day $ S \times 1.20^2 $ shoppers, and on the fourth day $ S \times 1.20^3 $ shoppers. The total number of shoppers over the first 4 days is given as 671. We can set up the equation as follows: $$ S + S \times 1.20 + S \times 1.20^2 + S \times 1.20^3 = 671 $$Set Up Equation: First, factor out $ S $ from the left side of the equation: $$ S(1 + 1.20 + 1.20^2 + 1.20^3) = 671 $$ Now calculate the sum inside the parentheses: $$ 1 + 1.20 + 1.20^2 + 1.20^3 = 1 + 1.20 + 1.44 + 1.728 $$ $$ = 5.368 $$ So the equation simplifies to: $$ S \times 5.368 = 671 $$Factor Out S: Now, divide both sides of the equation by 5.368 to solve for $ S $: $$ S = \frac{671}{5.368} $$ $$ S \approx 125.046 $$ Since the number of shoppers must be a whole number, we round to the nearest integer. $$ S \approx 125 $$

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