SOLUTION: I am trying to help my daughter with an algebra review sheet and I can not figure out how to do this problem. a/2 + C = 19 a/4 - 3C = -8 Find a thank you very much, Lydia

Algebra ->  Expressions-with-variables -> SOLUTION: I am trying to help my daughter with an algebra review sheet and I can not figure out how to do this problem. a/2 + C = 19 a/4 - 3C = -8 Find a thank you very much, Lydia       Log On


   

Question 8017: I am trying to help my daughter with an algebra review sheet and I can not figure out how to do this problem.
a/2 + C = 19
a/4 - 3C = -8
Find a
thank you very much,
Lydia Waller
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
Since there are two numbers that are represented by "unknowns" (C and a) you can try to find out what C is and then use it to find a.
The first equation says
a%2F2+%2B+C+=+19
a%2F2+=+19+-+C [subtracting C from both sides]
a%2F2+-+19+=+-C [subtracting 19 from both sides]
C+=+19+-+a%2F2 [multiplying both sides by -1 and rearranging]
This value for C can be put into the second equation
a%2F4+-+3C+=+-8
a%2F4+-3%2819+-+a%2F2%29+=+-8 [putting 19-a/2 for C]
a%2F4+-+57+%2B+3a%2F2+=+-8 [multiplying each term in the group by -3]
a%2F4+-+57+%2B+6a%2F4+=+-8 [getting a common denominator of 4 for the fractions]
7a%2F4+-+57+=+-8 [adding the fractions]
7a%2F4+=+49 [adding 57 to both sides]
7a+=+196 [multiplying both sides by 4]
a+=+28 [dividing both sides by 7]
Now put the value for a in the equation for C
C+=+19+-+28%2F2+=+19+-+14+=+5
Checking:
28/2 + 5 = 14 + 5 = 9
28/4 - 15 = 7 - 15 = -8