Determine 25341

In a two-digit number, the number of tens is three more than the number of ones. If we multiply the original number by a number written with the same digits but in the reverse order, we get the product 3 478. Determine the actual number.

Correct answer:

x =  74

Step-by-step explanation:

a=3+b (a 10+b) (a+10 b)=3478  (a 10+(a3)) (a+10 (a3))=3478  (a 10+(a3)) (a+10 (a3))=3478 121a2363a3388=0 121=112 363=3112 3388=227112 GCD(121,363,3388)=112=121  a23a28=0  p=1;q=3;r=28 D=q24pr=3241(28)=121 D>0  a1,2=2pq±D=23±121 a1,2=23±11 a1,2=1.5±5.5 a1=7 a2=4  a>0  a=a1=7 b=a3=73=4  x=a 10+b=7 10+4=74

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