# How do you solve 5/16y + 3/2y = 2 + 1/4y?

May 21, 2018

$\frac{32}{25}$

#### Explanation:

$\frac{5}{16} y + \frac{3}{2} y = 2 + \frac{1}{4} y$

Make your denominator the same
$\frac{5}{16} y + \frac{24}{16} y = 2 + \frac{4}{16} y$

Move your “y” to one side
$\frac{29}{16} y - \frac{4}{16} y = 2$

Simplify
$\frac{25}{16} y = 2$

Multiply both sides by $\frac{16}{25}$
$y = 2 \times \frac{16}{25}$

Simplify
$y = \frac{32}{25}$

May 21, 2018

$y = \frac{32}{25} = 1.28$

#### Explanation:

$\frac{5}{16} y + \frac{3}{2} y = 2 + \frac{1}{4} y$

Multiply all the terms by the least common multiple of the three denominators, which is $16$.

$\left(16\right) \frac{5}{16} + \left(16\right) \frac{3}{2} y = \left(16\right) 2 + \left(16\right) \frac{1}{4} y$

Now cancel out all of the terms to simplify:

stackrelcolor(red)1cancel16 5/cancel(16)y + stackrelcolor(red)8 cancel(16)3/cancel2y = 32 + stackrelcolor(red)4cancel16 1/cancel4y

$\textcolor{red}{1} \left(5\right) y + \textcolor{red}{8} \left(3\right) y = 32 + \textcolor{red}{4} \left(1\right) y$

$5 y + 24 y = 32 + 4 y$

$29 y = 32 + 4 y$

$25 y = 32$

$y = \frac{32}{25} = 1.28$