Question

Creating and solving equationstwo-thirds a number plus 4 is 7

Answer 1

Given:

two-thirds a number plus 4 is 7

First Part: Converting the statement into equation

Let x be the number in the given statement.

The phrase "two-thirds a number" can be expressed as

`(2)/(3)x`

Pair it with "... plus 4" and we get

`(2)/(3)x+4`

Finally, it is stated it is equal to 7, and we complete the equation

`(2)/(3)x+4=7`

Second Part: Solving for the number

Now, that we have the equation, we can now solve for the missing number x.

Subtract both sides by 4, to remove the constant 4 on the left side of the equation

`\begin{gathered} (2)/(3)x+4=7 \\ (2)/(3)x+4-4=7-4 \\ (2)/(3)x\cancel{+4-4}=3 \\ (2)/(3)x=3 \end{gathered}`

Multiply both sides by 3/2, and we get

`\begin{gathered} (2)/(3)x=3 \\ (2)/(3)x\cdot(3)/(2)=3\cdot(3)/(2) \\ \frac{\cancel{2}}{\cancel{3}}x\cdot\frac{\cancel{3}}{\cancel{2}}=(9)/(2) \\ x=(9)/(2) \end{gathered}`

Therefore, the number is 9/2 or nine-halves.