, 2026

Multiplying both sides of the equation by $2 \cdot 3 = 6$, we obtain $6 \cdot \dfrac{2t}{3} + 6\cdot\dfrac{3t}{2} = 6 \cdot 26$ or $4t + 9t = 156$.

Simplifying, we obtain $13t = 156$ and so $t = 12$. Alternatively, using a common denominator of $2 \cdot 3 = 6$, we obtain $\dfrac{2 \cdot 2t}{2 \cdot 3} + \dfrac{3 \cdot 3t}{3 \cdot 2} = 26$ or $\dfrac{4t}{6} + \dfrac{9t}{6} = 26$. Simplifying, we obtain $\$\dfrac{13t}{6}$ =
26$and so$13t = 6 $\cdot$ 26$or$t = 6 $\cdot$ 2 = 12. Multiplying both sides of the equation by

8$, we obtain$$\dfrac{8(3+x)}{4}$ = 6 + x$which simplifies to$2(3+x) = 6 + x$. Simplifying further, we obtain$6 + 2x = 6 +
x$and so$x = 0. Alternatively, splitting each fraction into two pieces, we obtain

$\dfrac{3}{4} + \dfrac{x}{4} = \dfrac{6}{8} + \dfrac{x}{8}$$. Since$$\dfrac{3}{4} = \dfrac{6}{8}$$, we obtain$$\dfrac{x}{4} = \dfrac{x}{8}$$and so$8x = 4x$or$x = 0$. Since$y > 0$, then$$\sqrt{y^2}$ = y. From the given equation, we obtain

$\sqrt{9}$ +
16 + 144} = $\sqrt{9}$ + 16} + y$. Thus,$$\sqrt{169} = \sqrt{25}$ + y$or$13 = 5 + y$and so$y = 8$.