Answer:
[tex]t=1\frac{1}{3}[/tex]
Step-by-step explanation:
we have
[tex]22t=32(2\frac{1}{4}-t)[/tex]
Solve for t
That means ----> isolate the variable t
Convert mixed number to an improper fraction first
[tex]2\frac{1}{4}=\frac{2*4+1}{4}=\frac{9}{4}[/tex]
substitute
[tex]22t=32(\frac{9}{4}-t)[/tex]
Multiply by 4 both sides to remove the fraction
[tex]88t=32(9-4t)[/tex]
Distribute right side
[tex]88t=288-128t[/tex]
Adds 128t both sides
[tex]88t+128t=288[/tex]
[tex]216t=288[/tex]
Divide by 216 both sides
[tex]t=\frac{288}{216}[/tex]
Simplify
[tex]t=\frac{4}{3}[/tex]
Convert to mixed number
[tex]\frac{4}{3}=\frac{3}{3}+\frac{1}{3}=1\frac{1}{3}[/tex]
therefore
[tex]t=1\frac{1}{3}[/tex]
