Question

Suzie's budget is: hop+on+the+bus=gus
Knowing that each letter stands for a different digit 0 through 9 and no two letters stand for the same digit. How much money did Suzie request?

Answer 1

ok im working on it... heres what i got so far, hop+on+the=gus-bus ( us -us) has to equal the letters for zero, whitch also means that op+on+he = 00

Answer 2

thanks for working on it... I trying to come up with an answer based on your tips so far

Answer 3

i shouold say op+on+he = a number that has zero in the digit and tens place

Answer 4

[(h)*10^2]+[(o)*10^1]+[(p)*10^0]+[(o)*10^1]+[(n)*10^0]+[(t)*10^2]+[(h)*10^1]+[(e)*10^0]=(g-b)x10^2

Answer 5

[(h)*100]+2[(o)*10]+p+n+[(t)*100]+[(h)*10]+e=(g-b)x100

Answer 6

reading your reply...

Answer 7

Sorry... what number does each letter represent?

Answer 8

im not sure, what i did is assume that xyz as a number in this system would correspond to x = the hundreds value, y = tens, and z = digit, so i sorted them out like that, now im going to try to divide it out

Answer 9

110h+20o+p+n+100t+e=100g-100b, this is proabally as far as i can get lol im gonna keep trying

Answer 10

what class is this for:? linear algebra?

Answer 11

Algebra 1 in 7th grade

Answer 12

working through your reply now...

Answer 13

7th grade algebra!?

Answer 14

i think my methods are too abstract!, im at a loss, im sorry

Answer 15

yes... but this is a high school credit even though I am in 7th grade. crazy, I know.

Answer 16

actually, you are helping me think about it in a different way... thanks.

Answer 17

@jim_thompson5910

Answer 18

@phi

Answer 19

This is just something where you have to use trial and error

notice that p+n+e+s = xs

where the x is the carry

The carry will be larger than 0 because you're starting at some number s and you're looping back to s. The only way to do this is if the carry is at least 1.

Answer 20

oh and because you're dealing with single digit numbers, x = 1 because there's no possible way to have a carry larger than 1

Answer 21

this would then mean

1+o+n+h+u = yu

where y is the new carry, again because we start from u and end back at u, we must have carry, which is also 1

Answer 22

finally one last thing to realize is the sum is a 3 digit number, so the sum of the hundreds digits must not exceed 10 (keep the carry in mind)

Answer 23

thanks @jim_thompson5910