Question 295158: I've been trying to get the answer, but it keeps coming out wrong. The question is "The sum of three numbers is 25. The sum of the first two numbers is 17 less than the third. The third number is 6 more than the second. Find the sum of the second and third numbers." It's a multiple choice answer. (a)4 ,(b)10 ,(c)36 ,(d)15 , and (e)21. The point I'm trying to get across is that the teacher told us the answer, and he said it was (c)36, but I disagree, for the sum of three numbers is 25, so how could two numbers equal 36?
I've only managed to get this down:
a+b+c=25 ; a+b=c-17; c=b+6.
Unfortunately, I do not know where else to go from there, and I would really appreciate your help. Thank you.
Found 2 solutions by mananth, Theo:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! "The sum of three numbers is 25. The sum of the first two numbers is 17 less than the third. The third number is 6 more than the second. Find the sum of the second and third numbers." It's a multiple choice answer. (a)4 ,(b)10 ,(c)36 ,(d)15 , and (e)21. The point I'm trying to get across is that the teacher told us the answer, and he said it was (c)36, but I disagree, for the sum of three numbers is 25, so how could two numbers equal 36?
let thenumbers be x. y , z
x+y+z=25
x+y+17= z
z=y+6
x+y+z=17--------------- equation 1
x+y-z=-17-------------- equation 2
z-y=6------------------ equation 3
add equation 2 and equation 3
x+y-z +z-y=-17+6
x=-9
Plug the value of x in equation 1 and equation 2
-9+y+z=17
-9+y-z=-17
Add these two equations
-18+2y==0
2y=18
y=9
plug the values of x and y in equation1
-9+9+z=25
z=25
x=-9 , y=+9 , z=25
y+z=36.
In your argument you have to remember that there can be negative numbers.
Have fun
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! Your answer is:
a = -11
b = 15
c = 21
Here's how:
You set a, b, c equal to your numbers. a is the first, b is the second, c is the third.
Your equations are:
a + b + c = 25 (equation 1)
a + b = c - 17 (equation 2)
c = b + 6 (equation 3)
Substitute (b + 6) for c in equations 1 and 2 to get:
a + b + (b + 6) = 25 (equation 1.1)
a + b = (b + 6) - 17 (equation 2.1)
Simplify equation 1.1 as follows:
Equation 1.1 is equal to:
a + b + (b + 6) = 25
Remove parentheses to get:
a + b + b + 6 = 25
Combine like terms to get:
a + 2b + 6 = 25
Subtract 6 from both sides of the equation to get:
a + 2b = 19 (equation 1.2)
Simplify equation 2.1 as follows:
Equation 2.1 is equal to:
a + b = (b + 6) - 17
Remove parentheses to get:
a + b = b + 6 - 17
Subtract b from both sides of this equation to get:
a = 6 - 17
Combine like terms to get:
a = -11 (equation 2.2)
You now have the following equations:
a + 2b = 19 (equation 1.2)
a = -11 (equation 2.2)
c = b + 6 (equation 3)
Substitute -11 for a in equation 1.2 to get:
a + 2b = 19 becomes:
-11 + 2b = 19
Add 11 to both sides of this equation to get:
2b = 30
Divide both sides of this equation by 2 to get:
b = 15 (equation 1.3)
You now have:
b = 15 (equation 1.3)
a = -11 (equation 2.2)
c = b + 6 (equation 3)
Substitute 15 for b in equation 3 to get:
c = b + 6 becomes:
c = 15 + 6 which becomes:
c = 21 (equation 3.1)
You now have:
a = -11 (equation 2.2)
b = 15 (equation 1.3)
c = 21 (equation 3.1)
These should be your numbers.
You confirm by going through the original 3 equations using these numbers to see if they are true.
Equation 1:
a + b + c = 25 becomes -11 + 15 + 21 = 25 which becomes -11 + 36 = 25 which becomes 25 = 25 which is true.
Equation 2:
a + b = c - 17 becomes -11 + 15 = 21 - 17 which becomes 4 = 4 which is true.
Equation 3:
c = b + 6 becomes 21 = 15 + 6 which becomes 21 = 21 which is true.
All 3 original equations are true, so your numbers must be:
a = -11
b = 15
c = 21
The sum of the second 2 numbers is 15 + 21 = 36.
That's your answer.
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