Question

Faye and Andrew have written down the same negative number.

Faye squares the number then multiplies by 2 and adds 4.
Andrew multiples the number by 21 then subtracts the result from 40.
They both finish with the same answer. What was the number?

Answer 1

x - the number

Faye squares the number: x²
then multiplies by 2: 2x²
and adds 4: 2x²+4

Andrew multiplies the number by 21: 21x
then subtracts the result from 40: 40-21x

They both finish with the same answer, so the results are equal.

`2x^2+4=40-21x \\ 2x^2+21x+4-40=0 \\ 2x^2+21x-36=0 \\ 2x^2+24x-3x-36=0 \\ 2x(x+12)-3(x+12)=0 \\ 2x-3=0 \ \lor \ x+12=0 \\ 2x=3 \ \lor \ x=-12 \\ x=(3)/(2) \ \lor \ x=-12`

The number is negative so x=-12.

The number is -12.