Letters can replace numbers in simple mathematical problems. If E and F represent digits and EF + F = FE, then F equals
A. 3
B. 6
C. 8
D. 9
How best can I resolve this problem such that it will be clear to grade six pupils.
Thanks
Hi Plato
I've got another issue:
I believe the range of possible answers:{0,1,2,3,4,5,6,7,8,9} were selected based on the equation: 9E = 8F.
So if the equation had been something like
1.9R = 9S
As such R and S=1
The possible range must be: {0,1,2,3,4,5,6,7,8,9}
2.For 10x = 8y
The range of possible answers will be: {0,1,2,3,4,5,6,7,8,9,10}
I hope I'm right?
The range of E and F was not selected based on the equation 9E = 8F. The problem statement says, "E and F represent digits." Therefore, . In fact, since the problem statement uses two-digit numbers FE and EF, neither E nor F can be 0. Further, 9E = 8F implies that 8F is divisible by 9. But since the GCD(8, 9) = 1, (a generalization of) Euclid's lemma says that F must be divisible by 9. Since F is an integer between 1 and 9, F must be 9. It is also possible to go through all possible variants for F and see for which one 8F is divisible by 9.