Question

algebra 1.2 section a checkpoint

1. a hair - stylist job pays $20 per hour and $5 per haircut.

a. describe any variables needed to write an equation to represent how much the hair stylist makes in a day of work. choose a letter to represent each variable. for example, \e\ is the amount of money earned that day.
b. write an equation using the variables that you selected to represent how much the hair stylist makes in a day of work.

1. the equation 4s + t = 100 represents the number of students, s, and teachers, t, who go on a field trip.

a. what does it mean that s = 22 and t = 12 is a solution to the equation?
b. how could you use a graph representing the equation to find another solution?

Explanation:

1. Problem 1 - Part a

Define variables for income - related quantities. Let $h$ be the number of hours worked and $c$ be the number of haircuts given.

2. Problem 1 - Part b

The hair - stylist earns $20$ per hour and $5$ per haircut. The total amount of money $E$ earned in a day is the sum of the money earned from hours worked and haircuts given.
$E = 20h+5c$

3. Problem 2 - Part a

A solution to the equation $4s + t=100$ means that when $s = 22$ (number of students) and $t = 12$ (number of teachers), the left - hand side of the equation equals the right - hand side.
Substitute $s = 22$ and $t = 12$ into the left - hand side: $4\times22+12=88 + 12=100$. It means that when there are 22 students and 12 teachers, the total number of people going on the field trip satisfies the given relationship.

4. Problem 2 - Part b

The graph of the equation $4s + t=100$ (which can be rewritten as $t=-4s + 100$, a linear equation) is a straight line. Any point $(s,t)$ on the line is a solution to the equation. To find another solution, locate another point on the line. For example, set $s = 0$, then $t=100$; set $t = 0$, then $4s=100$ or $s = 25$. We can read the coordinates of other points on the line from the graph.

Answer:

1. a. Let $h$ be the number of hours worked and $c$ be the number of haircuts given.

b. $E = 20h+5c$

1. a. When $s = 22$ and $t = 12$, substituting into $4s + t$ gives $4\times22+12=100$, which means that 22 students and 12 teachers satisfy the relationship for the number of people on the field trip.

b. Locate other points on the graph of the line $t=-4s + 100$. Points on the line are solutions to the equation.