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c=3d-274d+10c=120 solving using substitution

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2 Answers

c=3d - 27
4d + 10c = 120
 
Since we know what 'C' is equal to (Given c=3d-27), we can plug that into the second equation, giving us:
4d+10(3d-27)=120
 
We multiple the parenthetical out with the factor in front of it
4d+30d-270=120
 
Combine like terms
34d-270=120390
 
Add 270 from both sides:
(34d-270)+270=(120)+270
34d=390
 
Then we divide both sides by 34:
(34d)/34=(-390)/34
 
d= - 390/34
 
We can simplify that to:
 
d= 195/17
 
Make this a proper fraction:
 
d=11 8/17 
 
Now we know the value of D!
 
So we plug D back into the first equation
 
c=3d-27
 
c=3(11 8/17) -27
 
Multiply the parenthetical:
c=34 7/17 - 27
 
and then combine the terms:
 
c =7 7/17
 
Hope that helped!!!
Because c = 3d - 27, we can replace "c" with "3d - 27"
So in the equation 4d + 10c = 120 we can replace c (as stated above)
to get the equation 4d + 10(3d - 27) = 120
Now we have an equation with one variable and can solve for d.
 
4d + 10(3d - 27) = 120    [distribute]
4d + 30d - 270 = 120    [combine like terms]
34d - 270 = 120    [add 270]
34d = 390    [divide by 34]
d = 390/34    [simplify]
d = 195/17
 
Now to solve for c, pick either original equation, plug in the value of d, and solve for c. (The one where c is isolated is easier to use.)
c = 3d - 27
c = 3(195/17) - 27
c = 585/17 - 27
c = 585/17 - 459/17
c = 126/17