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

$\left \{ {{ 11\frac{9}{10}+3\frac{2}{5}=15\frac{3}{10}} \atop { 11\frac{9}{10}-3\frac{2}{5}=8\frac{5}{10}}} \right.$

To solve for this, you can create a series of two equations
$\left \{ {{y+x=15 \frac{3}{10} } \atop {y-x= 8\frac{5}{10} }} \right.$

After that, you solve one of the equations for x and plug it into the other equation.
$\left \{ {{x=15 \frac{3}{10}-y } \atop {y-x= 8\frac{5}{10} }} \right.$

${2y-15 \frac{3}{10}= 8\frac{5}{10}$

Then, solve for variable y
${2y=23 \frac{8}{10}$
${y=11\frac{9}{10}$

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

$11\frac{9}{10}+x=15 \frac{3}{10}$

$x=15 \frac{3}{10} -11\frac{9}{10}$

$x=3 \frac{2}{5}$