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# The Ruizes offer each of their children two different options for increasing the child’s weekly allowance. Option 1: Increase the allowance by one half of the current allowance. Option 2: Increase the allowance by $3 per week. Describe under what conditions each option is preferable. Justify your answers. Solution Verified Answered 2 years ago Answered 2 years ago Step 1 1 of 2 It is given that the children can either choose: Option 1: increase their allowance by half of their current allowance Option 2: increase it by $\3$ The option that gives the largest increase is the more preferable option. This means the first option is only preferable if half of their current allowance is more than $\3$ and the second option is only preferable if half of their current allowance is less than $\3$. Let $x$ be their current allowance. Then we need to find when $\dfrac{1}{2}x>3$ to find when Option 1 is preferable. Since $\dfrac{1}{2}\cdot6=3$, then $\dfrac{1}{2}x>3$ when $x>6$. Therefore,$\textbf{Option 1 is preferable if their current allowance is more than $\boldsymbol{\6}$ and Option 2 is preferable if their current allowance is less than $\boldsymbol{\6}$}\$.

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