Pampering and Feeding Time

Learning Focus

Use systems of equations to schedule time and share limited resources.

Big idea

Scheduling and resource problems usually have two constraints: how many and how much (time, food, money).

• Let each variable stand for a quantity of one type.
• Equation 1 counts items; Equation 2 totals the resource.
• Solve by substitution or elimination and check units.

Worked example

A groomer has $130$ minutes for $5$ pets. A bath takes $20$ min, a trim takes $30$ min. Let $b$ = baths, $t$ = trims.

• $b+t=5$
• $20b+30t=130$
• $20(5-t)+30t=130 \Rightarrow 100+10t=130 \Rightarrow t=3$, $b=2$.

Check: $40+90=130$.

Takeaways

• One equation counts, one totals the resource.
• Keep units consistent (minutes, cups, dollars).
• Check in both equations.