Question

(5y+1)/4+(3y+2)/16=3

Answer 1

$\frac{5y+1}{4} +\frac{3y+2}{16} =3|*16\\4*(5y+1)+3y+2=48\\20y+4+3y+2=48\\23y+6=48\\23y=42 |:23\\y=\frac{42}{23}.$

Answer 2

To solve the equation $\frac{{5y+1}}{4} + \frac{{3y+2}}{16} = 3$, we can follow these steps:

Step 1: Find a common denominator for the fractions. In this case, the common denominator is 16.

Step 2: Rewrite both fractions with the common denominator (16).

Step 3: Combine the fractions on the left side of the equation.

Step 4: Solve for y.

Let's go through each step:

Step 1: The common denominator is 16.

Step 2: Rewrite the fractions with the common denominator (16):

$\frac{{5y+1}}{4} = \frac{{(5y+1) \times 4}}{4 \times 4} = \frac{{20y + 4}}{16}$

$\frac{{3y+2}}{16} = \frac{{3y+2}}{16}$

Step 3: Combine the fractions on the left side of the equation:

$\frac{{20y + 4}}{16} + \frac{{3y + 2}}{16} = \frac{{20y + 4 + 3y + 2}}{16} = \frac{{23y + 6}}{16}$

Step 4: Now, we have the equation:

$\frac{{23y + 6}}{16} = 3$

To solve for y, we can cross-multiply:

$23y + 6 = 3 \times 16$

$23y + 6 = 48$

Now, isolate y:

$23y = 48 - 6$

$23y = 42$

$y = \frac{42}{23}$

This is the simplified value for y. If you need a decimal approximation, it is approximately $y \approx 1.826$.