Question

Find two mixed numbers so that the sum is 15 3/10 and the difference is 8 5/10

Answer 1

11 9/10 and 3 2/5


`\left \{ {{ 11(9)/(10)+3(2)/(5)=15(3)/(10)} \atop { 11(9)/(10)-3(2)/(5)=8(5)/(10)}} \right.`

To solve for this, you can create a series of two equations

`\left \{ {{y+x=15 (3)/(10) } \atop {y-x= 8(5)/(10) }} \right.`

After that, you solve one of the equations for x and plug it into the other equation.

`\left \{ {{x=15 (3)/(10)-y } \atop {y-x= 8(5)/(10) }} \right.`


`{2y-15 (3)/(10)= 8(5)/(10)`

Then, solve for variable y

`{2y=23 (8)/(10)`

`{y=11(9)/(10)`

Then, you plug in this value for y into one of the original equations


`11(9)/(10)+x=15 (3)/(10)`


`x=15 (3)/(10) -11(9)/(10)`


`x=3 (2)/(5)`