need help????

Question

lucy is thinking of a number,less than 50,with the decimal part in tenths.If she switches the tens and tenths digit,the number increases by 39.6.If she instead switches the tenths and ones digit,the number increases by 1.8.What is the original number?

Answer 1

let the number be ab.c

10a+b+0.1c

10c+b+0.1a=10a+b+0.1c+39.6

10a+c+0.1b=10a+b+0.1c+1.8

subtract the second equation from the first equation

9c+0.9b-9.9a=37.8

9(c+0.1b-1.1a)=37.8

divide both sides by 9

c+0.1b-1.1a=4.2

c+0.1b-1a-0.1a=4.2

(c-a)+0.1(b-a)=4.2

c-a=4 and b-a=2

the number must be less than 50 so (a) can be 4,3,2, or 1

if a=4 then substitute into c-a=4 to get c-4=4 which means c=8

if a=4 then substitute into b-a=2 to get b-4=2 which means b=6

the number is ab.c=46.8

switch 4 and 8 to get 86.4=46.8+39.6

switch 6 and 8 to get 48.6=46.8+1.8

the original number is 46.8