THe second of three numbers is 5 less than 4 times the first. The third is 9 less than twice the first. If 4 times the third os decreased by the first, the result is 6. find the three numbers.
S=4F-5
T=2F-9
4T-F=6
does that help?
1st number = x,
2nd number = 4x - 5,
3rd numbe = 2x - 9,
4(2x - 9) - x 6,
8x - 36 - x = 6,
7x 42,
x = 6 = 1st number.
(4x - 5) = 4*6 - 5 = 19 = 2nd number.
(2x - 9) = 2*6 - 9 = 3 = 3rd number.
.
CORRECTION:
4(2X - 9) - X = 6.
To solve this problem, let's assign variables to the three unknown numbers. We'll call the first number "x," the second number "y," and the third number "z."
According to the given information, we can write the following equations:
1. The second number is 5 less than 4 times the first: y = 4x - 5
2. The third number is 9 less than twice the first: z = 2x - 9
3. Four times the third number decreased by the first is equal to 6: 4z - x = 6
Now, we have a system of three equations with three variables. We can solve this system using substitution or elimination method:
Using substitution:
1. Substitute y from equation 1 into equation 3:
4z - x = 6
4(2x - 9) - x = 6
8x - 36 - x = 6
7x - 36 = 6
7x = 42
x = 6
2. Substitute the value of x back into equation 1 to find y:
y = 4x - 5
y = 4(6) - 5
y = 24 - 5
y = 19
3. Substitute the value of x back into equation 2 to find z:
z = 2x - 9
z = 2(6) - 9
z = 12 - 9
z = 3
Therefore, the three numbers are x = 6, y = 19, and z = 3.