# How do you solve (7t + 7)/4 + (7t + 8)/3 = 33?

Nov 29, 2015

$t = 7$

#### Explanation:

Multiply both sides by $12$ because $4$ and $3$ are factors of $12$

$12 \left(\frac{7 t + 7}{4} + \frac{7 t + 8}{3}\right) = 33 \left(12\right)$

$3 \left(7 t + 7\right) + 4 \left(7 t + 8\right) = 396$

Distribute the $3$ and $4$

$21 t + 21 + 28 t + 32 = 396$

Combine like terms

$49 t + 53 = 396$

Subtract $53$ from both sides

$49 t = 343$

Divide both sides by $49$

$t = 7$

Now check to see if $t = 7$ gives $33$

$\frac{7 \left(7\right) + 7}{4} + \frac{7 \left(7\right) + 8}{3} = 33$

$\frac{49 + 7}{4} + \frac{49 + 8}{3} = 33$

$\frac{56}{4} + \frac{57}{3} = 33$

$14 + 19 = 33$