Pet Sitters

Learning Focus

Write and solve a system of linear equations that models a service with two constraints (total count and total money).

Big idea

A system of linear equations pairs two equations that must be true at the same time. When a service has a total count constraint and a total amount constraint, define one variable per type of item and write one equation for each constraint.

• Substitution: solve one equation for a variable, then replace it in the other.
• Elimination: add or subtract equations to cancel a variable.
• The solution $(x,y)$ is the point where the two graphs intersect.

Worked example

A sitter makes $10$ visits in a day. A dog walk pays 12 dollars and a cat visit pays 8 dollars. She earns 96 dollars. How many of each?

Let $w$ = walks and $c$ = cat visits.

• Count: $w+c=10$
• Money: $12w+8c=96$
• Substitute $c=10-w$: $12w+8(10-w)=96 \Rightarrow 4w+80=96 \Rightarrow w=4$
• Then $c=6$. Check: $12(4)+8(6)=48+48=96$.

Takeaways

• Define a variable for each type of item.
• Write one equation per constraint (count and money).
• Check the solution in both equations.