Algebra Word Problems

Word Problems:  Word problems are verbal explanations of problems that can be solved using math.

Strategy:

The most important strategy is to read the problem line by line and sentence by sentence and write down all the relevant material in an abbreviated way.  Then, one can decide on the most efficient approach.

Example:  There are 250 students in a class of which some are boys and some are girls.  The class is interested in buying tickets to the Denver Nuggets games to watch Iverson play. Since most of the interest in buying tickets comes from the boys, the tickets for boys are 10 dollars and the tickets for girls are only 5 dollars. If the class spends a total of 2000 dollars, how many boys and how many girls are in the class?.

So, following strategy, we see that:

number of boys = b, number of girls = g, b+g = 250 because there are 250 students.

10b+5g = 2000 because it costs 10 dollars per ticket for boys and 5 dollars for girls and the total amount is 2000.

*Notice that it doesn't matter that "they are going to watch the Nuggets nor does it matter that they would like to watch Iverson".  In addition, it is irrelevant that boys are more interested in the game. We have extracted all the important information and we have done so reading line to line.  In the briefest way of writing the pertinent information, we have these two equations:

10b+5g = 2000    and
b+g = 250.  

Here, you notice that we can solve this problem using substitution or elimination.  Lets apply substitution for simplicity.

b+g = 250 means b = 250–g    so, substituting this in the other equation, we get

10(250–g)+5g = 2000
2500–10g+5g = 2000
2500–5g = 2000
500 = 5g

Lastly, we divide by 5 on both sides to get that g = 100 and since the total number of boys and girls was 250, it leaves us with 150 = b, so 150 boys and 100 girls.

This is basically the approach that one should take in solving word problems.