Expert: Paul Klarreich - 5/22/2007

Question
I am taking grade 11 applied math.
Can you give me the steps to solving this word problem?
You own a poodle. The cost of food for your dog is $50.00. Hair grooming sessions cost $10 each. You have budgeted $300 for expenses for your dog. How many grooming sessions can you afford?

Answer
Questioner:   Doug

Question:  I am taking grade 11 applied math.
Can you give me the steps to solving this word problem?
You own a poodle. The cost of food for your dog is $50.00. Hair grooming sessions cost $10 each.  You have budgeted $300 for expenses for your dog.

How many grooming sessions can you afford?
.........................................
Hi, Doug,

First step: Make sure to include ALL details in the problem, such as:

You have budgeted $300 EACH MONTH for expenses for your dog.

Next:  Rewrite the question in numeric terms.  Instead of

"How many grooming sessions each month can you afford?"

write:

"What is the number of grooming sessions each month you can afford?"

That is the trick.  NEVER write "How many" or "How much".  ALWAYS write "What is the number of..."

That focuses the issue on a number to be found.  After that, it is easy to give that number a name:

Let  g = the number of grooming sessions per month

and draw conclusions:

Then  10g = the cost of the grooming sessions each month.

And  50 + 10g is the total of the expenses each month.

But that is 300.

So you have an equation:

50 + 10g = 300

and you are on your way home.  Solve the equation:

10g = 250
g = 25

and state the answer verbally:

I can afford 25 grooming sessions.

You can then draw a practical conclusion, like an engineer submitting a report and recommendation:

DON'T BUY A POODLE.

(You did say this was applied math, didn't you?)