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
please help me
To find the three numbers, let's define variables for each of them. Let's call the first number X, the second number Y, and the third number Z.
Based on the given information, we can create equations to represent the relationships between the numbers:
1) "The second of three numbers is 1 less than the first."
This can be expressed as: Y = X - 1
2) "The third number is 5 less than the second."
This can be expressed as: Z = Y - 5
3) "The first number is twice as large as the third."
This can be expressed as: X = 2Z
Now, we can solve these equations simultaneously to find the values of X, Y, and Z.
Let's substitute equation 3 into equation 1:
Y = 2Z - 1 (eq. A)
Now substitute equation 2 into equation A:
Z = (2Z - 1) - 5
Simplifying:
Z = 2Z - 6
Z - 2Z = -6
-Z = -6
Z = 6
Now, we can substitute the value of Z into equation 2 to find Y:
Y = 6 - 5
Y = 1
Finally, we can substitute the value of Z into equation 3 to find X:
X = 2(6)
X = 12
Therefore, the three numbers are:
X = 12
Y = 1
Z = 6