Question

represent systems by graphing
use the graph comparing the cost of two laundry services to answer problems 1–3. each service charges a fixed fee and a price per pound of laundry.

1. compare the slopes. what does this tell you?
2. compare the y-intercepts. what does this tell you?
3. financial literacy which service offers a lower total price? explain.
4. compare the costs of two tablet computers. in addition to the cost of the tablet, there is a monthly data fee.

a. graph and label the equations on the coordinate plane shown.
b. financial literacy which tablet has a lower monthly data fee? explain.
c. construct arguments if the plan is to use the tablet for eight months, which tablet costs less overall? explain.
tablet computers
brand a: ( y = 50x + 100 )
brand b: ( y = 25x + 200 )
(graphs for laundry services and tablet computers are shown)

Explanation:

To solve the problem of determining which tablet (Brand A or Brand B) costs less over 8 months, we analyze the cost equations for each brand.

Step 1: Identify the cost equations

• For Brand A: \( y = 50x + 100 \)
• For Brand B: \( y = 25x + 200 \)

Here, \( x \) represents the number of months, and \( y \) represents the total cost in dollars.

Step 2: Calculate the total cost for Brand A over 8 months

Substitute \( x = 8 \) into the equation for Brand A:
\[

$$\begin{align*} y_{\text{Brand A}} &= 50(8) + 100 \\ &= 400 + 100 \\ &= 500 \end{align*}$$

\]

Step 3: Calculate the total cost for Brand B over 8 months

Substitute \( x = 8 \) into the equation for Brand B:
\[

$$\begin{align*} y_{\text{Brand B}} &= 25(8) + 200 \\ &= 200 + 200 \\ &= 400 \end{align*}$$

\]

Step 4: Compare the total costs

• Total cost for Brand A: \( \$500 \)
• Total cost for Brand B: \( \$400 \)

Since \( 400 < 500 \), Brand B (with the equation \( y = 25x + 200 \)) costs less over 8 months.

Answer:

Brand B (with the cost equation \( y = 25x + 200 \)) costs less over 8 months. The total cost for Brand A is \(\$500\) and for Brand B is \(\$400\).