SOLUTION: The following is known about three numbers: If the second number is subtracted from the sum of the first number and 5 times the third number, the result is -25. The third number pl
Algebra.Com
Question 139017: The following is known about three numbers: If the second number is subtracted from the sum of the first number and 5 times the third number, the result is -25. The third number plus of 4 times the first number is -4. The first number plus 4 times the second number plus the third number is 16. Find the three numbers.
[Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The following is known about three numbers: If the second number is subtracted from the sum of the first number and 5 times the third number, the result is -25. The third number plus of 4 times the first number is -4. The first number plus 4 times the second number plus the third number is 16. Find the three numbers.
;
Let the 3 numbers be x, y, z
:
Write an equation for each statement:
:
"If the second number is subtracted from the sum of the first number and 5 times the third number, the result is -25."
x + 5z - y = -25
:
"The third number plus 4 times the first number is -4."
z + 4x = -4
:
"The first number plus 4 times the second number plus the third number is 16."
x + 4y + z = 16
:
Find the three numbers.
:
Write the 3 equations in the standard form:
x - y + 5z = -25
4x +0y + z = -4
x + 4y + z = 16:
:
Subtract the 3rd equation from the 2nd equation
4x + 0y + z = -4
x + 4y + z = 16
------------------Subtracting eliminates z
3x - 4y + 0 = -20
3x - 4y = -20
:
Multiply the 2nd equation by 5, subtract the 1st equation:
20x + 0y + 5z = -20
x - 1y + 5z = -25
---------------------subtracting eliminates z
19x + y + 0 = +5
19x + y = +5
:
Multiply the above equation by 4 and add to the 1st "two unknown" equation:
3x - 4y = +20
76x +4y = -20
----------------adding eliminates y
79x + 0y = 0
x = 0
:
This makes it easy to find z using the 2nd equation:
z + 4(0) = -4
z = -4
:
Use the 1st equation to find y:
x + 5z - y = -25
0 + 5(-4) - y = -25
-20 - y = 025
-y = -25 + 20
-y = -5
y = +5:
:
We have x=0; y=5; z=-4
:
Check solutions in the 3rd equation
x + 4y + z = 16
0 + 4(5) - 4 = 16; confirms our solutions
RELATED QUESTIONS
the following is known about three numbers: three times the first number plus the second... (answered by ankor@dixie-net.com)
The following is known about three numbers: If the second number is subtracted from the... (answered by josgarithmetic,MathTherapy)
the following is known about three numbers: if the second number is subtracted from the... (answered by stanbon)
The following is known about three numbers:If the second number is subtracted from the... (answered by ankor@dixie-net.com)
The sum of twice a first number and three times a second number is 71. If the second... (answered by erica65404)
Please help....word problems are the death of me!!!!
The sum of three numbers is 1. If... (answered by josgarithmetic,ikleyn)
The sum of three times a first number and twice a second number is 8. If the second... (answered by mananth)
The sum of three times a first number, and twice a second number is 8. If the second... (answered by ankor@dixie-net.com)
The sum of three times a first number, and twice a second number is 14. If the second... (answered by josgarithmetic)