One number is (8) more than another. The sum of three times one and twice the other is (94). What is the smaller number?

(14)

Word problems become easier when the unknown quantities are represented by variables. Since one number is 8 greater than the other, the larger number can be written as the smaller number plus 8. The statement about three times one number and twice the other gives a second equation. Substituting the first relationship into that equation reduces the problem to one variable. The wording is consistent with taking the coefficient 3 for the larger number, as used in the supplied solution.

Let the smaller number be 
m y
m. Then the larger number is 
m x=y+8
m. The condition gives 
m 3x+2y=94
m. Substitute: 
m 3(y+8)+2y=94
m, so 
m 3y+24+2y=94
m and 
m 5y=70
m. Hence 
m y=14
m. The larger number is 22, and 
m 3(22)+2(14)=94
m, so option B is correct.

This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..