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23. The difference of four times a number and 7 is 15 plus the quotient of the number and 3. Which of the following equations could be used to find the value of [tex]x[/tex]?

A. [tex]4x - 7 = \frac{x}{3} + 15[/tex]

B. [tex]7 - 4x = \frac{x}{3} + 15[/tex]

C. [tex]7 - 4x = \frac{3}{x} + 15[/tex]

D. [tex]4x - 7 = \frac{3}{x} + 15[/tex]

Answer :

We start by letting [tex]$x$[/tex] be the number.

1. The phrase “four times a number” translates to [tex]$4x$[/tex].
2. “The difference of four times a number and 7” means we subtract 7 from [tex]$4x$[/tex], which gives us
[tex]$$4x - 7.$$[/tex]
3. The phrase “15 plus the quotient of the number and 3” means we add 15 to the result of dividing [tex]$x$[/tex] by 3, which gives us
[tex]$$15 + \frac{x}{3}.$$[/tex]
4. The word “is” indicates an equality, so we set the two expressions equal:
[tex]$$4x - 7 = 15 + \frac{x}{3}.$$[/tex]

This equation matches the one in option A.

Therefore, the correct option is A.

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