Solve (4)5(2/5x+4/5y)+4(51/4x+3/4y)

$$( 4 ) 5 ( \frac { 2 } { 5 } x + \frac { 4 } { 5 } y ) + 4 ( 5 \frac { 1 } { 4 } x + \frac { 3 } { 4 } y )$$

Evaluate

$$29x+19y$$

Solution Steps

Multiply 4 and 5 to get 20.

$$20\left(\frac{2}{5}x+\frac{4}{5}y\right)+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Use the distributive property to multiply 20 by \frac{2}{5}x+\frac{4}{5}y.

$$20\times \frac{2}{5}x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Express 20\times \frac{2}{5} as a single fraction.

$$\frac{20\times 2}{5}x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Multiply 20 and 2 to get 40.

$$\frac{40}{5}x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Divide 40 by 5 to get 8.

$$8x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Express 20\times \frac{4}{5} as a single fraction.

$$8x+\frac{20\times 4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Multiply 20 and 4 to get 80.

$$8x+\frac{80}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Divide 80 by 5 to get 16.

$$8x+16y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Multiply 5 and 4 to get 20.

$$8x+16y+4\left(\frac{20+1}{4}x+\frac{3}{4}y\right)$$

Add 20 and 1 to get 21.

$$8x+16y+4\left(\frac{21}{4}x+\frac{3}{4}y\right)$$

Use the distributive property to multiply 4 by \frac{21}{4}x+\frac{3}{4}y.

$$8x+16y+4\times \frac{21}{4}x+4\times \frac{3}{4}y$$

Cancel out 4 and 4.

$$8x+16y+21x+4\times \frac{3}{4}y$$

Cancel out 4 and 4.

$$8x+16y+21x+3y$$

Combine 8x and 21x to get 29x.

$$29x+16y+3y$$

Combine 16y and 3y to get 19y.

$$29x+19y$$

Expand

$$29x+19y$$

Solution Steps

Multiply 4 and 5 to get 20.

$$20\left(\frac{2}{5}x+\frac{4}{5}y\right)+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Use the distributive property to multiply 20 by \frac{2}{5}x+\frac{4}{5}y.

$$20\times \frac{2}{5}x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Express 20\times \frac{2}{5} as a single fraction.

$$\frac{20\times 2}{5}x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Multiply 20 and 2 to get 40.

$$\frac{40}{5}x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Divide 40 by 5 to get 8.

$$8x+20\times \frac{4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Express 20\times \frac{4}{5} as a single fraction.

$$8x+\frac{20\times 4}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Multiply 20 and 4 to get 80.

$$8x+\frac{80}{5}y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Divide 80 by 5 to get 16.

$$8x+16y+4\left(\frac{5\times 4+1}{4}x+\frac{3}{4}y\right)$$

Multiply 5 and 4 to get 20.

$$8x+16y+4\left(\frac{20+1}{4}x+\frac{3}{4}y\right)$$

Add 20 and 1 to get 21.

$$8x+16y+4\left(\frac{21}{4}x+\frac{3}{4}y\right)$$

Use the distributive property to multiply 4 by \frac{21}{4}x+\frac{3}{4}y.

$$8x+16y+4\times \frac{21}{4}x+4\times \frac{3}{4}y$$

Cancel out 4 and 4.

$$8x+16y+21x+4\times \frac{3}{4}y$$

Cancel out 4 and 4.

$$8x+16y+21x+3y$$

Combine 8x and 21x to get 29x.

$$29x+16y+3y$$

Combine 16y and 3y to get 19y.

$$29x+19y$$