Question
Question 7
(Multiple Choice Worth 2 Points)
(Systems of Linear Equations MC)
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $3, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 3 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 10 pounds will cost $17 for both options.
A package that weighs 7 pounds will cost $17 for both options.
A package that weighs 17 pounds will cost $31 for both options.
A package that weighs 17pounds will cost $37 for both options.
Answers
GPT-4o mini
To find out when the cost of the two shipping options will be the same, we need to set the two equations equal to each other:
1. For the first option: \( y = 3 + 2x \)
2. For the second option: \( y = 17 \)
Setting them equal:
\[ 3 + 2x = 17 \]
Now, we can solve for \( x \):
1. Subtract \( 3 \) from both sides:
\[ 2x = 17 - 3 \]
\[ 2x = 14 \]
2. Divide both sides by \( 2 \):
\[ x = 7 \]
So, the two shipping options will have the same cost when the package weighs **7 pounds**.
Now let's look at the provided options:
- A package that weighs 10 pounds will cost $17 for both options.
- **A package that weighs 7 pounds will cost $17 for both options.** (This is the correct answer.)
- A package that weighs 17 pounds will cost $31 for both options.
- A package that weighs 17 pounds will cost $37 for both options.
Therefore, the correct answer is: **A package that weighs 7 pounds will cost $17 for both options.**
1. For the first option: \( y = 3 + 2x \)
2. For the second option: \( y = 17 \)
Setting them equal:
\[ 3 + 2x = 17 \]
Now, we can solve for \( x \):
1. Subtract \( 3 \) from both sides:
\[ 2x = 17 - 3 \]
\[ 2x = 14 \]
2. Divide both sides by \( 2 \):
\[ x = 7 \]
So, the two shipping options will have the same cost when the package weighs **7 pounds**.
Now let's look at the provided options:
- A package that weighs 10 pounds will cost $17 for both options.
- **A package that weighs 7 pounds will cost $17 for both options.** (This is the correct answer.)
- A package that weighs 17 pounds will cost $31 for both options.
- A package that weighs 17 pounds will cost $37 for both options.
Therefore, the correct answer is: **A package that weighs 7 pounds will cost $17 for both options.**