To find the value of [tex]\( t \)[/tex] for which the expressions [tex]\(\left(\frac{21}{3}+\frac{1}{3}\right)\)[/tex] and [tex]\(\left(\frac{t}{3}-15\right)\)[/tex] become equal, we follow these steps:
1. Simplify the left-hand expression [tex]\(\left(\frac{21}{3}+\frac{1}{3}\right)\)[/tex]:
[tex]\[\frac{21}{3} + \frac{1}{3} = 7 + \frac{1}{3} = 7.333333333333333.\][/tex]
2. Set the left-hand side equal to the right-hand expression:
[tex]\[7.333333333333333 = \frac{t}{3} - 15.\][/tex]
3. Isolate [tex]\( \frac{t}{3} \)[/tex]:
Add 15 to both sides of the equation to isolate [tex]\(\frac{t}{3}\)[/tex]:
[tex]\[7.333333333333333 + 15 = \frac{t}{3}.\][/tex]
[tex]\[22.333333333333333 = \frac{t}{3}.\][/tex]
4. Solve for [tex]\( t \)[/tex]:
Multiply both sides of the equation by 3 to solve for [tex]\( t \)[/tex]:
[tex]\[t = 22.333333333333333 \times 3.\][/tex]
[tex]\[t = 67.\][/tex]
So, the value of [tex]\( t \)[/tex] for which the expressions [tex]\(\left(\frac{21}{3}+\frac{1}{3}\right)\)[/tex] and [tex]\(\left(\frac{t}{3}-15\right)\)[/tex] become equal is [tex]\( t = 67 \)[/tex].
