A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $4, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 4 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $12 to send the box, represented by the equation y = 12.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
a) A package that weighs 4 pounds will cost $12 for both options.
b) A package that weighs 8 pounds will cost $12 for both options.
c) A package that weighs 12 pounds will cost $20 for both options.
d) A package that weighs 12 pounds will cost $28 for both options.
To find when the cost of the two shipping options will be the same, we need to solve for when the two equations y = 4 + 2x and y = 12 are equal to each other.
Setting the two equations equal to each other, we get:
4 + 2x = 12
Subtracting 4 from both sides, we get:
2x = 8
Dividing by 2, we get:
x = 4
Therefore, a package that weighs 4 pounds will cost $12 for both options.
So, the correct answer is:
a) A package that weighs 4 pounds will cost $12 for both options.