In the 1st week of July record of 1100 people went to the local swimming pool. in the 2nd week 100 fewer people went to the pool then in the 1st week. in the 3rd week 145 more people went to the pool then in the 2nd week. In the 4th week 375 fewer people went to the pool then in the 3rd week .what Is the percentage decrease in the number of people who went to the pool over these 4 weeks?

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SorenO607378 SorenO607378 · Answer 1 · 2022-10-29T09:17:45+02:00

In the 1st week we have 1100 people. In the 2nd we have 1100-100=1000 people. In this week, the decrease was

[tex]\begin{gathered} 1100\text{ people ----100\%} \\ 1000\text{ people ---- x} \end{gathered}[/tex]

then, by the rule of three, we obtain

[tex]\begin{gathered} x=\frac{(1000)(100)}{1100} \\ x=90.91 \end{gathered}[/tex]

so the decrease was 100-90.91= 9.09%.

In the 3rd week, there was 145 more people than 2nd week. Then, we have 1000+145=1145. Therefore, with respect to the first week, we have

[tex]\begin{gathered} 1100\text{ people ---- 100\%} \\ 1145\text{ people --- x} \end{gathered}[/tex]

by the rule of three, we have

[tex]\begin{gathered} x=\frac{(1145)(100)}{1100} \\ x=104 \end{gathered}[/tex]

that is, with respect to the 1st week, we have an increment of 104-100=4%

Now, in 4th week, there was 375 fewer people than 3rd week. Hence, there was 1145-375= 770 people. Then, with respect to the first week, we obtain

[tex]\begin{gathered} 1100\text{people ----100\%} \\ 770\text{ people ---- x} \end{gathered}[/tex]

which gives

[tex]\begin{gathered} x=\frac{(770)(100)}{1100} \\ x=70 \end{gathered}[/tex]

so, the decrement wih respect to the 1st week was 100-70=30%