"The sum of two numbers is 15. Three times one of the numbers is 11 less than five times the other. Find the numbers."
I'm trying to write an equation for this that uses the same variable on both sides, but getting nowhere :'(
Can anyone help? Thanks!
2006-10-20 05:13:39 · 11 answers · asked by Anonymous in Education & Reference ➔ Homework Help
Let,one number be x ,then the other no is 15-x .The equation will be 3x=5(15-x)-11.Solve this equation and you get the answer which is 8 and 7.
2006-10-20 06:02:00 · answer #1 · answered by alpha 7 · 0⤊ 2⤋
let x be the first number
y be the second number
x + y = 15 --- equation 1
3x = 11 - 5y ---equation 2
Solution
solve for x in equation 2
x = (11 - 5y)/3--- equation 2a
substitute equation 2a in 1
(11-5y)/3 +y =15
multiply both sides of the equation by 3
(11-5y) + 3y = 3(15)
11 - 2y = 45
-2y = 45-11
-2y = 34
y = -17
solving for x, subtitute value of y in equation 1
x + (-17) = 15
x = 15 + 17
x = 32
Therefore the value of x =32 and y = -17
Checking
Substitute these values in equation 2
3x = 11 - 5y
3(32) = 11 - 5(-17)
96 = 11 + 85
96 = 96
2006-10-20 05:34:28 · answer #2 · answered by The young Merlin 4 · 1⤊ 0⤋
This is a sum in simultaneous equations and will require 2 variables.
the sum of 2 numbers is 15 = x + y = 15
3x one of the numbers is 11 less than 5x the other = 3x + 11 = 5y
Then bring letters to one side and numbers to another
3x - 5y = -11
work out simultaneously
3x - 5y = -11
x + y = 15
Multiply the bottom row by 5 to get rid of the y variable
3x - 5y = -11
5x + 5y = 75
8x -- = 64
x = 64 / 8
x = 8
if x = 8 and x + y = 15
then
8 + y = 15
y = 15 - 8
y = 7
2006-10-20 05:26:17 · answer #3 · answered by MAC C 3 · 0⤊ 1⤋
The sum of two numbers is 15.
let:
x + y = 15 -> eq 1.
Three times one of the numbers is 11 less than five times the other.
3x = 11 - 5y - > eq 2
then,
combining eq 1 and 2
x + y = 15
3x = 11 - 5y
or
x + y = 15
3x + 5y = 11
multiply eq 1 by 3 then subtract both equations.
3x + 3y = 45
3x + 5y = 11
-----------------
-2y = 34
y = -17
substituting y to eq 1
x + (-17) = 15
x = 32
there, a more detailed answer
2006-10-20 05:33:17 · answer #4 · answered by -=NiWrA=- 2 · 0⤊ 1⤋
let sum of two numbers x and y be written as
x + y = 15
Now, 3times x is equal to 5 times y less 11. which can be written as
3x=5y-11.
Now this equation can be rewritten as
3x-5y= -11.
solve both equations as follows(x ly 1st equation by 3 thruout)
3x +3y = 45
3x - 5y = -11
(-) (+) (+)
_______________
0x + 8y = 56
therefore y=7
substitue this value in one of the equations, you get x = 8.
Good luck!
2006-10-20 05:29:14 · answer #5 · answered by Jaaji 2 · 0⤊ 1⤋
x+y=15
3x=y-11 or 3x-y=11
multiply the first equation with three to make the factors same
3x+3y=45
subtract 2nd eq from 3rd eq.
2y=17. then x=15-17=-2.
2006-10-20 06:17:40 · answer #6 · answered by sumaravindran1958 2 · 0⤊ 1⤋
a+b=15
3a=(5b-11)
(5b-11)/3+b=15
a=7
b=8
2006-10-20 11:26:27 · answer #7 · answered by Super Girl 2 · 0⤊ 0⤋
this is the equation:
x + y = 15
3x = 5y - 11
x = 8
y = 7
2006-10-20 05:27:58 · answer #8 · answered by justpristine 2 · 0⤊ 1⤋
a+b=15
3a=(5b-11)
(5b-11)/3+b=15
a=7
b=8
2006-10-20 05:21:03 · answer #9 · answered by trudy_eiselman2007 1 · 0⤊ 1⤋
a+b=15
3a=(5b-11)
(5b-11)/3+b=15
a=7
b=8
2006-10-20 05:17:34 · answer #10 · answered by Anonymous · 0⤊ 1⤋