Question

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

(x: number of small purses made.
y: number of big purses made.)

Answer 1

The inequality which represents the solution is: 2x + 3y ≤ 18

Explanation:

In the inequality, there are some important words

• If the value is at least, that means the sign of inequality is ≥

• If the value is minimum, that means the sign of inequality is ≥

• If the value is at most, that means the sign of inequality is ≤

• If the value is maximum, that means the sign of inequality is ≤

∵ The number of small purses = x

∵ Sarah takes 2 hours to make small purses

→ She takes 2x hours

∵ The number of big purses = y

∵ She takes 3 hours to make big purses

→ She takes 3y hours

∴ She takes a total of 2x + 3y hours

∵ She has a maximum of 18 hours a week

→ That means the sign of inequality is ≤

∴ 2x + 3y ≤ 18

The inequality which represents the solution is: 2x + 3y ≤ 18