Video: Using Linear Equations to Solve Problems

Fourteen subtracted from three-fifths of a number is twenty-two. What is the number?

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Video Transcript

14 subtracted from three-fifths of a number is 22. What is the number?

If we let the number equal 𝑥, we can set up an equation to solve this problem. Three-fifths of the number would be written three-fifths 𝑥 or three-fifths multiplied by 𝑥. We want to subtract 14 from this number. This gives us three-fifths of 𝑥 minus 14. The answer is 22. Therefore, this expression is equal to 22. Three-fifths of 𝑥 minus 14 is equal to 22.

Multiplying both sides of the equation by five can eliminate the fraction. Three-fifths multiplied by five is equal to three. 14 multiplied by five is equal to 70. And 22 multiplied by five is 110. This leaves us with the equation three 𝑥 minus 70 equals 110.

Adding 70 to both sides of this equation gives us three 𝑥 equals 180, as 110 plus 70 is 180. Finally, dividing both sides by three gives us a value of 𝑥 equal to 60. This means that the number is 60. 14 subtracted from three-fifths of 60 is equal to 22.

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