Math CentralQuandaries & Queries


Question from Linda:

four less than three times a number is 20, what is the number?

Hi Linda,

Suppose you knew the number, for example suppose the number is 7. The instructions then say

four less than three times a number.

If the number is 9 then 3 times the number is $3 \times 9$ and "four less than three times the number" is $3 \times 9 - 4.$ (If 9 were the correct then this would be 20 which it is not.)

In algebra we pretend we know the number, give it a name and repeat the steps above. I am gong to name the unknown number $n.$ In that case 3 times the number is $3 \times n$ and 4 less than 3 times the number is $3 \times n - 4.$ The problem states that the result of this calculation is 20 and hence

\[3 \times n - 4 = 20.\]

Solve for $n.$

Once you have $n$ you can verify your answer. Calculate $3 \times n - 4.$ Did you get 20?


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