Three friends, Nakobe, Mikah, and Ashton, are saving up money to buy microphones for their podcast. The total cost of the microphones is represented by the expression 9x2 − 3x + 4.
The friends have already saved the following amounts:
Nakobe: x2
Mikah: x − 12
Ashton: 3x + 4
Which expression represents the amount of money the friends still need to buy the microphones?
To find the amount of money the friends still need to buy the microphones, we need to subtract the total cost of the microphones from the sum of the amounts that each friend has saved.
The sum of the amounts saved by the three friends is:
Nakobe: x^2
Mikah: x - 12
Ashton: 3x + 4
Adding these expressions together, we get:
x^2 + x - 12 + 3x + 4
Simplifying, we get:
4x^2 + 4x - 8
This represents the total amount of money the three friends have saved. To find the amount of money they still need to buy the microphones, we need to subtract the cost of the microphones (9x^2 - 3x + 4) from this total.
So the expression that represents the amount of money the friends still need to buy the microphones is:
4x^2 + 4x - 8 - (9x^2 - 3x + 4)
Simplifying, we get:
-5x^2 + 7x - 12
Therefore, the answer is -5x^2 + 7x - 12.
To determine the amount of money the friends still need to buy the microphones, we need to find the difference between the total cost of the microphones and the amount each friend has already saved.
The total cost of the microphones is represented by the expression 9x^2 - 3x + 4.
Nakobe has already saved x^2.
Therefore, the amount Nakobe still needs to save is (9x^2 - 3x + 4) - x^2.
Mikah has already saved x - 12.
Therefore, the amount Mikah still needs to save is (9x^2 - 3x + 4) - (x - 12).
Ashton has already saved 3x + 4.
Therefore, the amount Ashton still needs to save is (9x^2 - 3x + 4) - (3x + 4).
The expression representing the amount of money the friends still need to buy the microphones is:
(9x^2 - 3x + 4) - x^2 for Nakobe,
(9x^2 - 3x + 4) - (x - 12) for Mikah, and
(9x^2 - 3x + 4) - (3x + 4) for Ashton.