2. Anita multiplies a number by 2 and then adds her starting number to the product. Amit adds this same original number to itself and then multiplies that sum by 2. The difference between Anita’s and Amit’s results is 9. What is their starting number?Explain.
To solve the problem, we need to set up equations based on the given information and then solve for the starting number.
Let's say the starting number is "x".
According to the first statement, Anita multiplies the number by 2 and then adds her starting number to the product: 2x + x = 3x.
According to the second statement, Amit adds the original number to itself and then multiplies that sum by 2: 2(2x) = 4x.
The difference between Anita's and Amit's results is 9: 3x - 4x = -x = 9.
To find the starting number, we solve the equation -x = 9:
Divide both sides of the equation by -1 to isolate "x":
x = -9.
Therefore, their starting number is -9.
starting number --- x
Anita's method
2x + x = 3x
Amit:
(x+x)(2) = 4x
4x - 3x = 9
x = 9
My algebra becomes the explanation.
check:
Anita ---> 2(9) + 9 = 27
Amit ---> (9+9)(2) = 36
difference = 36-27 = 9
all is good!