one number is twice another number.if 15 is subtracted from the both numbers,then one of the new numbers becomes thrice that of the new number.find the numbers
What does math have to do with silversmithing?
smaller number ---- x
larger number ------2x
x-15 = 3(2x - 15)
x-15 = 6x - 45
-5x = -30
x = 6
the two numbers are 6 and 12
check:
6-15 = -9
12-15 = -3
and -9 is 3 times the -3
All is good
To solve this problem, let's assign variables to the numbers.
Let's say the first number is x, and the second number is y.
According to the problem statement, "one number is twice another number," so we can express it as:
x = 2y
Also, it states that "if 15 is subtracted from both numbers, then one of the new numbers becomes thrice that of the new number." We can express this as:
(x - 15) = 3(y - 15)
Now we have a system of two equations. We can solve it to find the values of x and y.
Substituting x = 2y into the second equation:
(2y - 15) = 3(y - 15)
Now, let's solve for y:
2y - 15 = 3y - 45
-15 + 45 = 3y - 2y
30 = y
Now, substitute the value of y back into the equation x = 2y:
x = 2(30)
x = 60
Therefore, the first number (x) is 60, and the second number (y) is 30.