One possible method to solve for B, C, and P is to use substitution and some algebraic manipulation. Here are the steps:
1. Use the second equation to express B in terms of P:
B/P = 4/5
B = (4/5)P
2. Substitute this expression for B into the first and third equations:
C + B + P = 103
C + (4/5)P + P = 103
Simplify:
C + (9/5)P = 103
[C - 1/2C + B - 1/2B + P] = 79
C/2 + B/2 + P = 79
Substitute B = (4/5)P:
C/2 + (2/5)P + P = 79
Simplify:
C/2 + (7/5)P = 79
3. Use the first equation to express C in terms of P:
C = 103 - B - P
Substitute B = (4/5)P:
C = 103 - (4/5)P - P
Simplify:
C = 103 - (9/5)P
4. Substitute the expressions for B and C into the equation for C + (9/5)P:
(103 - (9/5)P) + (9/5)P = 103
Simplify:
4/5 P = 4
P = 5
5. Use this value of P to find B and C:
B = (4/5)P = 4(4/5) = 3.2
C = 103 - B - P = 103 - 3.2 - 5 = 94.8
Therefore, the solution is B = 3.2, C = 94.8, P = 5.
C + B + P==103,
B/P ==4/5,
[C - 1/2C + B - 1/2B + P]==79, solve for B, C, P
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