Answer
more than $35$ pounds
Work Step by Step
Let $x$ be the weight of the laundry.
The given conditions translate to
\begin{array}{l}\require{cancel}
15\lt0.50(10)+0.40(x-10)
.\end{array}
Using the properties of inequality, then
\begin{array}{l}\require{cancel}
15\lt5+0.40(x)+0.40(-10)
\\\\
15\lt5+0.40x-4
\\\\
15\lt1+0.40x
\\\\
-0.40x\lt1-15
\\\\
-0.40x\lt-14
\\\\
x\gt\dfrac{-14}{-0.40}
\\\\
x\gt35
.\end{array}
Hence, when the weight of the laundry is $\text{
more than $35$ pounds
,}$ the housekeeper is more economical than the laundromat.
