Question

Kyle wants to know which company has a better price for different numbers of jerseys. Which statement correctly compares the total costs of the companies?
Guy's Graphix and Patty's Printing both cost the same for 9 jerseys.
O Patty's Printing costs less than Guy's Graphix for any number of jerseys.
O Patty's Printing costs $20 less than Guy's Graphix for 20 jerseys.
O Guy's Graphix costs $12 less than Patty's Printing for 6 jerseys.

Answer 1

I don't have the graph or the companies' cost formulas, so I can't tell which statement is correct yet. Send the picture of the graph or the cost equations (or the table of values) and I’ll pick the correct statement and show the work.

If you want to check it yourself, here’s how to decide:

1. Read each company's line on the graph and write its cost function:
- Identify the y-intercept (fixed/startup cost) and the slope (cost per jersey). So C_G(x) = m_G x + b_G and C_P(x) = m_P x + b_P.

2. To check “both cost the same for 9 jerseys,” compute C_G(9) and C_P(9). If equal, that statement is true.

3. To check “Patty’s costs less than Guy’s for any number of jerseys,” compare slopes and intercepts:
- If C_P(x) < C_G(x) for all x ≥ 0 then Patty’s slope and intercept make it always lower (you can check by seeing if the two lines never cross and Patty’s is below Guy’s at two sample x-values).
- Otherwise the lines cross or one is sometimes higher.

4. To check a specific-number claim (20 or 6 jerseys), just compute the two costs:
- Example check for 20 jerseys: compute Δ(20) = C_P(20) − C_G(20); if Δ(20) = −20 then “Patty’s is $20 less” is true.
- For 6 jerseys: compute Δ(6) = C_G(6) − C_P(6); if Δ(6) = 12 then “Guy’s is $12 less” is true.

If you upload the graph or give the two linear equations, I’ll compute the values and tell you which of the four statements is correct.