Question

as president of the student council, meg is choosing between two options for class t - shirts. a local shop charges $11 for each shirt, plus a set - up fee of $100. an online store charges $15 for each shirt, plus a set - up fee of $24. which equation can you use to find s, the number of shirts meg would need to order for the two options to cost the same? $11 + 100s = 15 + 24s$ $11s + 100 = 15s + 24$ how many shirts would meg need to order for the two options to cost the same? shirts

Explanation:

First Sub - Question (Equation Selection)

Step1: Analyze local shop cost

The local shop charges $11 per shirt and a $100 set - up fee. If the number of shirts is \(s\), the total cost \(C_1\) for the local shop is the cost per shirt times the number of shirts plus the set - up fee. So \(C_1=11s + 100\).

Step2: Analyze online store cost

The online store charges $15 per shirt and a $24 set - up fee. If the number of shirts is \(s\), the total cost \(C_2\) for the online store is \(C_2 = 15s+24\).

Step3: Set costs equal

To find when the two options cost the same, we set \(C_1 = C_2\), so the equation is \(11s + 100=15s + 24\).

Step1: Start with the equation

We have the equation \(11s+100 = 15s + 24\).

Step2: Subtract \(11s\) from both sides

\(11s+100-11s=15s + 24-11s\), which simplifies to \(100 = 4s+24\).

Step3: Subtract 24 from both sides

\(100 - 24=4s+24 - 24\), so \(76 = 4s\).

Step4: Divide both sides by 4

\(\frac{76}{4}=\frac{4s}{4}\), which gives \(s = 19\).

Answer:

\(11s + 100 = 15s + 24\)

Second Sub - Question (Number of Shirts)