2. Answers to Rates Problems

Answer to Rate Q1:  

The question is asking for “how many word problems”, hence we need to show the rate with the number of word problems on top

Knowing the rate, we use it and the total time allowed in the test to determine the quantity of problems:

Answer to Rate Q2:

The rate we are looking for is "5 word problems in about 12 minutes.  This can be described as 5 word problems/12 minutes, or 12 minutes to grade 5 word problems.  The problem is asking for time - how long will it take.  So use the rate with minutes on top.

Use this rate to now solve for the time to do 25 problems.

We know the time for grading one test (which is a rate of 60 minutes/1 test)...now use that time to grade 25 tests.  In this case, I converted 60 minutes to one hour...

30 hours....Yikes!

Answer to Rate Q3

The problem is asking for the total number of questions required.  Hence, specify the rate as so many questions/minute

Knowing the time (minutes) before the end of class, solve for the quantity of questions needed to fill up the remaining time:

Answer to Rate Q4:  

There are two ways to solve this one.  The first method is brute force:  find the number of hard questions, then the number of medium questions, then subtract them both from the total (30) to find the remaining easy questions.  This method is the more traditional approach, and probably the method Common Core is looking for.

The alternative approach (which you can do nearly in your head) is to find the percentage of easy problems.  Percentages always add up to 100.  If we have 30/100 hard and 40/100 medium, then that leaves 30/100 remaining to make up the total 100/100, which are the easy ones.  Since the percentage of easy ones (30%) are the same percentage as the hard ones (30%), then the answers are the same:  9.

Answer to Rate Q5:  

Again, two ways to solve this one.  Find the quantity of boys (60% of 30), then subtract that from the total to find the remaining quantity of girls...or...find the percentage of girls (since the total percentage must add up to be 100), then calculate for the quantity of girls.

Answer to Rate Q6:  

This one is tricky.  The problem is asking for the total quantity of word problems solved correctly by the 18 boys versus the 12 girls. There are more boys than girls, so the total number of correct answers may be higher for the boys...except percentage of correct answers is lower than the girls.

So first, let's find the total quantity of problems being attempted by the girls, then figure out how many of those are correctly solved (in this case 60% for the girls).

Since there are 30 problems in the test, and 12 girls taking the test, then the total quantity of problems being attempted is 30 word problems x 12 girls = 360 girl word problems.

Now, if only 60% of them were solved correctly:  60% x 360 = 216 correct girl answers

Now the boys:  Total boy word problems = 30 word problems x 18 boys = 540

Quantity of Boys correct answers = 40% x 540 = 216 correct boy answers

It’s a Tie!!