Convert the mixed numbers to the improper fractions:
[tex]2\dfrac{3}{4}=\dfrac{2\cdot4+3}{4}=\dfrac{11}{4}\\\\19\dfrac{1}{4}=\dfrac{19\cdot4+1}{4}=\dfrac{77}{4}[/tex]
[tex]2\dfrac{3}{4}a=19\dfrac{1}{4}\\\\\dfrac{11}{4}a=\dfrac{77}{4}\qquad\text{multiply both sides by 4}\\\\\not4^1\cdot\dfrac{11}{\not4_1}a=\not4^1\cdot\dfrac{77}{\not4_1}\\\\11a=77\qquad\text{divide both sides by 11}\\\\\boxed{a=7}[/tex]
