Question

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?

Answer 1

2,000 problems

Explanation:

We know the students solved the following amount of problems:

Week 1 - 25% of the month

Week 2 - 110% of the first week--> this means 25(1.10)=27.5%

Week 3 - 60% of the first two week--> this means 0.6(25+26.5)=31.5%

Week 4 - 320 problems --> this is 16% of the quota since 100-25-27.5-31.5=16%

So we know that 320 is 16%. We can set up a proportion to find the total amount.

`(16)/(100) =(320)/(y)`

We solve by cross multiplying by multiplying numerator and denominator on opposite fractions.

`16(y)=100(320)\\16y=32000\\(16y)/(16)=(32000)/(16)\\  y=2,000`

The quota for the month is 2,000 problems.