## Real World Applications – Algebra I

### Topic

How can we represent how much a person earns making clothes in Bangladesh?

### Student Exploration

Bangladesh is one of the most popular countries for outsourcing labor because the labor is so cheap. Let’s apply our knowledge of linear equations to represent this relationship.

A child makes $20 per month for in a garment factory. Since this is a rate, this is the slope for our equation. Let’s say he/she would work every day out of the 30 days of the month. Our slope would then be represented as \begin{align*}\tfrac{\$20}{30\text{ days}},\end{align*}

From this example, we have both the slope \begin{align*}\left(\tfrac{2}{3}\right)\end{align*}

\begin{align*} y &= mx + b\\ 24 &= \left(\frac{2}{3}\right)(21) + b\\ 24 &= \frac{42}{3} + b\\ 24 &= 14 + b\\ 10 &= b\\ y &= \left(\frac{2}{3}\right)x + 10\end{align*}

In this equation, the “10,” or the “\begin{align*}b\end{align*}” value represents how much the child had before he started working. This equation is in slope-intercept form.

If we were to represent this equation in standard form, we first want to get the \begin{align*}x-\end{align*}term on the same side as the \begin{align*}y-\end{align*}term.

\begin{align*}\left(\frac{2}{3}\right)x + y = 10\end{align*}

We also want all whole numbers in our equation. Let’s multiply every term by “3” so the denominator disappears.

We now have \begin{align*}2x + 3y = 30\end{align*}

### Extension Investigation

Try finding the equation of the line in both slope-intercept form and standard form with the following information.

The child’s family found out that their child started saving money and thought it was a good idea and started saving too. One parent decided that all of her earnings are going toward their savings, and the other parent’s earnings will go toward the family’s expenses. The mother earns $36 per month. After 60 days, the family has $82.