Math CentralQuandaries & Queries


Question from Briana:

When 4 times the number increased by 30, the answer is the same as when 70 decreased by the number. What was my number?

Hi Briana,

I am going to call the unknown number $N.$

Four times the number is $4 \times N$ and then four times the number increased by 30 is

\[4 \times N + 30.\]

70 decreased by the number is

\[70 - N.\]

The problem says that these two quantities are the same so set them equal to form an equation and solve for $N.$

I think this is what is expected but without punctuation in the phrase "4 times the number increased by 30" it's hard to know for sure. I read it as "4 times the number, increased by 30" but you could read it as "4 times, the number increased by 30" in which case the first expression would be

\[4\times (N + 30).\]


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