## Related questions with answers

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

VerifiedIt 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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