Math CentralQuandaries & Queries


Question from monica, a student:


In your equations n is the number of brochures and C is the cost, one for each company. If the costs for the two companies are the same then

15 + 0.10n = 0.25n

Solve for n.

Hi Monica,

With an algebraic equation you can perform a mathematical operation on one side as long as you perform the same operation on the other side. In your problem I want to subtract 0.10n from the left side since that will remove any terms involving n from the left side. This operation is valid as long as I also subtract 0.10n from the right side. Thus I have

15 + 0.10n = 0.25n
15 + 0.10n - 0.10n= 0.25n - 0.10n
15 = 0.15n

You can now divide both sides by 0.15 to leave only n on the right side but I prefer to eliminate the decimal point before I divide. I do this by multiplying each side by 100 to get

15 = 0.15n
100 × 15 = 100 × 0.15n
1500 = 15n

Now divide both sides by 15 to get

1500 = 15n
1500/15 = 15n/15
100 = n


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