Question

At Kirn’s Kuts Hair Salon, the cost of a child’s haircut (x) is $10 and the cost of an adults hair cut (y) is $20. The managers goal for the day is to have at least 5 Childs cuts at least 10 adults cuts and gave total sales be at least $400. Write a system of inequalities to represent this situation.

Answer 1

`x \geq 5\\y \geq 10\\10x+20y\geq 400`

Explanation:

System of inequalities

Inequality is a relationship between variables in which the right side is not equal to the left side.

We know the cost of a child’s haircut is $10, let's call x the number of child’s haircuts done in one day. The sales for a child’s haircut will be 10x.

We also know the cost of an adult's hair cut is $20. If y is the number of adults hair cuts, then the sales for adults hair cuts is 20y

These are the restrictions.

We need to have at least 5 Childs cuts, i.e.

`x \geq 5`

We also need to have at least 10 adults cuts, i.e.

`y \geq 10`

The total sales must be at least $400, i.e.

`10x+20y\geq 400`

These 3 inequalities form the system required in the question