Simplify 310x + 16y + 310x + 36y

Question

3
10
𝑥

+

1
6
𝑦

+

3
10
𝑥

+

3
6
𝑦
. Be sure to reduce any fractions to the lowest terms.(1 point) .....

Answer 1

To simplify the expression \( 310x + 16y + 310x + 36y \), start by combining like terms.

1. Combine the \( x \) terms: \[ 310x + 310x = 620x \]

2. Combine the \( y \) terms: \[ 16y + 36y = 52y \]

3. Now, combine both results: \[ 620x + 52y \]

Next, look for any fractions in your original prompt involving \( \frac{3}{10}x \) and \( \frac{1}{6}y + \frac{3}{6}y \):

\[ \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \]

1. Combine the \( x \) terms: \[ \frac{3}{10}x + \frac{3}{10}x = \frac{6}{10}x = \frac{3}{5}x \]

2. Combine the \( y \) terms: \[ \frac{1}{6}y + \frac{3}{6}y = \frac{1+3}{6}y = \frac{4}{6}y = \frac{2}{3}y \]

3. Thus, the simplified expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]

So the simplified expression for \( 310x + 16y + 310x + 36y \) is \( 620x + 52y \) and for \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \) is \( \frac{3}{5}x + \frac{2}{3}y \).