Question 834990
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.