SOLUTION: In the first week students at a school solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems they solved last

Question 834990: In the first week students at a school solved 25 percent of their monthly quota of problems. In the second week, they solved 110 percent of the number of problems they solved last week. In the third week they solved 60 percent of the number of problems they solved in the first 2 weeks. In the 4th week, they solved the remaining 320 problems. How many problems did the students solve in the four week month?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of problems solved in the month.
in the first week they solved .25 * x
in the second week they solved 1.10 * .25 * x
in the third week they solved .6 * (.25 * x + 1.10 * .25 * x)
in the fourth week they solved 320.

simplify each week to get:

first week = .25x
second week = 1.10 * .25 * x = .275x
third week = .6 * (.12 * x + 1.10 * .25 * x) which is equal to:
.6 * .25 * x + .6 * 1.10 * .25 * x which is equal to:
.15 * x + .165 * x which is equal to:
.315 * x.
third week = .315x
fourth week = 320

add the first 3 weeks together and you get:
.25x + .275x + .315x = .84x

add the fourth week and you get:
all 4 weeks = .84x + 320

the sum of all 4 weeks must equal to the total number of problemsin the month.
we had initially set that up as being represented by x.
the equation is therefore:
.84x + 320 = x
subtract .84x from both sides of this equation to get:
320 = .16x
divide both sides of this equation by .16 to get:
320 /.16 = x
simplify to get:
x = 2000

that's your answer.

you can confirm by replacing x in the original equations and you will see that the sum of all of them is equal to 2000.

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