Answer
a = 123 and c = 291
Steps Explained:
Use the substitution method to solve:
2a + 1.75c = 755.25
Check Format
Equation 2 is in the correct format.
Rearrange Equation 2 to solve for a:
2a + 1.75c = 755.25
Subtract 1.75c from both sides to isolate a:
2a + 1.75c - 1.75c = 755.25 - 1.75c
2a = 755.25 - 1.75c
Now divide by 2:
| 2a | |
| 2 |
| = |
| 755.25 - 1.75c |
| 2 |
Plug Revised Equation 2 value into a:
1(a) + c = 414
1 * ((755.25 - 1.75c)/2) + c = 414
((755.25 - 1.75c)/2) + c = 414
Multiply equation 1 through by 2
2 * (((755.25 - 1.75c)/2) + c = 414)
2 * (((755.25 - 1.75c)/2) + c = 414)
755.25 - 1.75c + 2c = 828
Group like terms:
-1.75c + 2c = 828 - 755.25
0.25c = 72.75
Divide each side by 0.25
| 0.25c | |
| 0.25 |
| = |
| 72.75 |
| 0.25 |
| c = | 72.75 |
| 0.25 |
c = 291
Plug this answer into Equation 1
1a + 1(291) = 414
1a + 291 = 414
1a = 414 - 291
1a = 123
Divide each side by 1
| 1a | |
| 1 |
| = |
| 123 |
| 1 |
| a = | 123 |
| 1 |
a = 123
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