If a plus b=3, a plus c=5, b plus c=7, what is the value of a plus b-c???

Question

help me out with this.....please.....

Answer 1

-1.5

Answer 2

There may be quicker ways to solve this problem, but hopefully by showing a step-by-step approach, this answer will be more educational. We start with four equations that are in the original question.

(#1) a + b = 3
(#2) a + c = 5
(#3) b + c = 7
(#4) a + b - c = ?



Step One
Take equation 3. and subtract b from both sides. That produces a new equation 5.
(#5) c = 7 - b


Step Two
Now use equation 5 to substitute for c in equation 2. This gives us a new equation 6.
a + (7 - b) = 5
(#6) a - b = -2


Step Three
Combine equation 1 and equation equation 6 together. This will give us the value for a.
(a + b) + (a - b) = (3) + (-2)
2a = 1
a = 0.5


Step Four
Use the value for a to find the values for b. Start with equation 1...
a + b = 3
0.5 + b = 3
b = 2.5


Step Five
Use the value for a to find the value for c. Start with equation 2...
a + c = 5
0.5 + c = 5
c = 4.5


Step Six
Use the values for a, b and c to find to complete equation 4.
a + b - c = 0.5 + 2.5 - 4.5
a + b - c = - 1.5

Answer 3

#1=> A + B = 3
#2=> A + C = 5
#3=> B + C = 7

Solving for A in #1,
A = 3 - B

Substituting for A in #2,
( 3 - B ) + C = 5

Simplifying #2,
-B + C = 2

Adding simplified #2 and #3 together
( -B + C ) + ( B + C ) = 7 + 2

After simplifying, we get
C = 4.5

Plug the C value back into the original #2 and
A = 0.5

Plug the A value back into the original #1 and
B = 2.5

We are looking for A + B - C = ?, so plugging the known values
0.5 + 2.5 - 4.5 = -1.5

Hope this helps

Answer 4

Substitute so: b=3-A and c=5-A

Therefore 3-A + 5-A = 7
Solve this by adding the integers 3+5 and the variables -A +-A.

So 8 -2A = 7
-2A = -1 A= 1/2

Then substitute back into the original.

A = 1/2 B = 2 1/2 C = 4 1/2 Check the results :)

B - C = -2

Answer 5

This is a systems of equations prob...

Easily solved as below...

a + b = 3 so, b = 3 - a
a + c = 5 so, a = 5 - c

therefore b = 3 - 5 + c = c - 2

and b + c = 7 so, c-2 + c = 7...

solving for c we get, c = 4.5
so a = .5 and b = 2.5

therefore....

b-c = -2

blacklisted's answer is also very good.

Answer 6

I believe most are incorrect. First, get like terms.

a+b=3
a+c=5
b+c=7

You know that

(a+b)+(a+c)=8 therefore 2a=(8-b-c) then a=(8-b-c)/2

You now want to eliminate the b or the c

c=7-b therefore you can have a=((8-b)-(7-b))/2

the b's cancel since you are subtracting like signs

leaving a=1/2

1/2 + b = 3
b=2.5

2.5 + c = 7
c=4.5

so a+b-c would be .5+2.5-4.5= -1.5

your answer should be -1.5.

Answer 7

If I am not mistaken we need to get a+b-c not just b-c

then

a+b=3 --- 1
a+c=5 --- 2
b+c=7 --- 3

from 2 and 3 c=5-a and c=7-b adding the two we get

2c=(5+7)-(a+b)=12-3=9
2c=9
c=4.5

a+b-c=3-4.5=-1.5

Answer 8

a + b = 3
a + c = 5
b + c = 7

a + b = 3
a = -b + 3

a + c = 5
(-b + 3) + c = 5
-b + 3 + c = 5
-b + c = 2
c = b + 2

b + c = 7
b + (b + 2) = 7
b + b + 2 = 7
2b = 5
b = 2.5

c = 2.5 + 2 = 4.5
a = -(2.5) + 3 = -2.5 + 3 = .5

a + (b - c)
.5 + (2.5 - 4.5)
.5 + (-2)
.5 - 2
-1.5

ANS : -1.5

Answer 9

a+b=c --> b=3-a
a+c=5 --> c=5-a
b-c --> 3-a-(5-a)=3-5=-2

Answer 10

a+b=3 ------------> Equation 1
a+c=5 ------------> Equation 2
b+c=7 ------------> Equation 3

Subtract EQ 2 from EQ 1
(a+b)-(a+c) = 3-5
b - c = -2 ---------------> EQ 4

Add EQ1 & EQ2
(a+b)+(a+c)=3+5
2a + (b+c) = 8
2a + 7 = 8 (Used EQ 3 here)
2a = 8-7=1
a=1/2 = 0.5 -------------------> EQ 5

Add EQ 4 and EQ 5
a+(b-c) = 0.5 - 2
a+b-c = -1.5

Answer 11

a+b=3
a+c=5
subtracting
b-c=-2