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In the first week students at RSM solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems solved in the first week. In the third week they solved 60 percent of the number of problems they had solved in the first two weeks and, in the fourth week, they solved the remaining 320 problems. How many problems did students solve in the four-week month?

Respuesta :

Answer:

The number of problems solved = 2000

Step-by-step explanation:

Let us assume the monthly quota of problems be x

number of problem solved in first week = 25 % of x =[tex]0.25x[/tex]

number of problems solved in 2nd week = 110% of (problems solved in 1st       week)

                                                         = [tex]1.10 (0.25x)[/tex]

                                                         =[tex]0.275x[/tex]

number of problem solved 3rd week= 60% of ( problems solved in 1st and 2nd week)

                                                            = [tex]0.60(0.25x+0.275x)[/tex]

                                                            =[tex]0.60(0.525x)[/tex]

                                                            =[tex]0.315x[/tex]

number of problem solved in 4th week = [tex]320[/tex]

now we have

number of problems solved in ll 4 weeks = x

[tex]0.25x +0.275x+0.315x+320=x[/tex]

[tex]0.84x+320=x[/tex]

[tex]320=x-0.84x[/tex]

[tex]320=0.16 x[/tex]

[tex]x=\frac{320}{0.16}[/tex]

[tex]x=2000[/tex]

Hence the number of problems solved = 2000



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