The second of three numbers is 1 less than than the first. The third number is 5 less than the second. if the first number is twice as large as the third, find the three numbers.
write an equation and find the numbers
To find the three numbers, we can set up equations based on the given information.
Let's represent the first number as "x," the second number as "y," and the third number as "z."
According to the given information:
1) The second number is 1 less than the first:
y = x - 1
2) The third number is 5 less than the second:
z = y - 5
3) The first number is twice as large as the third:
x = 2z
Now, we can solve these equations simultaneously to find the values of x, y, and z.
Substituting equation 3) into equation 1), we have:
y = 2z - 1
Substituting equation 2) into equation 3), we have:
x = 2(y - 5)
x = 2y - 10
Substituting equation 3) into equation 2), we have:
z = (2z - 1) - 5
z = 2z - 6
6 = z
Now we can find the value of z. Plugging z = 6 into equation 3):
x = 2(6)
x = 12
Substituting z = 6 into equation 2):
x = 2y - 10
12 = 2y - 10
22 = 2y
y = 11
Therefore, the three numbers are:
x = 12
y = 11
z = 6