Gre math question I don't understand. If 3c+6d=24 and 4a+3d=18, what does A equal in terms of C?

Question

Repost, but i did it wrong before.

Answer 1

They are asking you to cancel out the variable d from the two simultaneous equations:

3c + 6d = 24 ................ (i)
4a + 3d = 18 .................(ii)

to leave an equation is just a and c. You then rearrange to place all terms in a on the LHS and c on RHS to leave a = f(c) - i.e. a as a function of c

To handle the simulataneous equations, you can use two techniques:

1) Elimination:

Starting with:

3c + 6d = 24 ................ (i)
4a + 3d = 18 .................(ii)

Multiply (ii) by -2 and add the equations together:

3c + 6d = 24 ................ (i)
-8a - 6d = -36 .................(ii)*-2
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3c - 8a + 0d = 24 - 36 = -12

So

8a - 3c = 12

And so rearranging

a = (12 + 3c)/8

Which is the answer

Or 2) Substitution:

Take (i) and rearrange to get just d on LHS and c on RHS:

3c + 6d = 24 ................ (i)

6d = 24 - 3c
d = 4 - c/2

And then substitute that for d in equation (ii):

4a + 3d = 18 .................(ii)
4a + 3*(4-c/2) = 18
4a + 12 - 3c/2 = 18
4a - 3c/2 = 6
8a - 3c = 12
a = (12 +3c)/8

The same answer as before

Answer 2

We need to find out about A
A is in only one equation

4a+3d=18
(separate out the a term)
4a+3d - 3d =18 - 3d
4a =18 - 3d
(simplify the a term)
4a / 4 =( 18 - 3d ) / 4
a =( 18 - 3d ) / 4

to find out anything more about a, we need to look at d
d is in one equation

3c+6d=24
(separate out the d term)
3c+6d - 3c =24 - 3c
6d = 24 - 3c
(simplify the a term)
6d / 6 = ( 24 - 3c ) / 6
d = ( 24 - 3c ) / 6
d = 4 - 1/2c

substitute this value of d into the simplified version of the first equation

a =( 18 - 3d ) / 4 && d = 4 - 1/2c
(locate the target)
a =( 18 - 3[d] ) / 4
(substitute)
a =( 18 - 3[ 4 - 1/2c ) ] / 4
(this should be simplified as well)

a is now in terms of c
or
the value of a is a function of the value of c

Answer 3

If 3c+6d=24 and 4a+3d=18, what does A equal in terms of C?
Multiply 2nd equation by -2 getting -8a -6d = -36
Add this result to 1st equation getting 3c -8a = -12
8a = 3c+12
a = (3c + 12)/8

Answer 4

First, you should notice that both equations contain a common variable, d. You must use this to your advantage. Solve the first equation for d in terms of c to get...

d = 4 - 1/2c

Next, solve the second equation for a in terms of d...

a = 18/4 - 3/4d.

Finally plug the value of d in terms of c into the equation for a and simplify...

a = 18/4 - 3/4(4 - 1/2c)
a = 18/4 - 3 + 3/8c

a = 3/2 + 3/8c

Answer 5

Multiply the second equation by 2.

8a+6d=36
3c+6d=24

Subtract the second from the first. Doesn't matter which is subtracted from which.

8a-3c=12
a=(12+3c)/8

Answer 6

6d = -3c + 24
d = -1/2c +4

4a+3(-1/2c+4) = 18

4a - 3/2c + 12 = 18
a = 3/2 + 3/8c

Answer 7

solve for a
4a+3d=18
4a=18-3d
a=18/4-3d/4

solve for d
3c+6d=24
6d=24-3c
d=4-(1/2)c

replace d with 4-(1/2)c
a=18/4-3/4(4-(1/2)c
a=18/4-12/4-3/8c
a=6/4-3/8c
a=3/2-3/8c

Answer 8

u have to substitute the value of a in c .