The difference of two numbers is 8. When twice the first number is added to three times the second number, the result is 51. What are the two numbers?
A.
12 and 4
B.
15 and 7
C.
20 and 12
D.
23 and 15
Let's call the first number x and the second number y.
According to the first condition, the difference of the two numbers is 8, so we can write the equation:
x - y = 8 ----(1)
According to the second condition, when twice the first number is added to three times the second number, the result is 51, so we can write the equation:
2x + 3y = 51 ----(2)
To solve this system of equations, we can use the first equation to express x in terms of y:
x = y + 8
Substituting this expression for x into the second equation, we get:
2(y + 8) + 3y = 51
2y + 16 + 3y = 51
5y + 16 = 51
5y = 35
y = 7
Substituting this value of y back into the first equation, we can solve for x:
x - 7 = 8
x = 15
Therefore, the two numbers are 15 and 7.
The correct answer is B. 15 and 7.