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

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- Oct 1st 2012, 03:27 AMKayPeeLetters used in place of numbers
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 - Oct 1st 2012, 04:02 AMPlatoRe: Letters used in place of numbers
- Oct 1st 2012, 04:17 AMTwoPlusTwoRe: Letters used in place of numbers
Edit: Plato beat me to it (plus I was wrong (Giggle))

- Oct 1st 2012, 04:57 AMKayPeeRe: Letters used in place of numbers
- Oct 1st 2012, 05:51 AMemakarovRe: Letters used in place of numbers
- Oct 1st 2012, 07:57 AMKayPeeRe: Letters used in place of numbers
- Oct 1st 2012, 08:06 AMKayPeeRe: Letters used in place of numbers
- Oct 1st 2012, 08:11 AMPlatoRe: Letters used in place of numbers
- Oct 1st 2012, 08:27 AMKayPeeRe: Letters used in place of numbers
- Oct 1st 2012, 10:33 AMKayPeeRe: Letters used in place of numbers
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? - Oct 1st 2012, 11:08 AMPlatoRe: Letters used in place of numbers
- Oct 1st 2012, 11:41 AMemakarovRe: Letters used in place of numbers
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, $\displaystyle 0\le E,F\le 9$. 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.