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# At what point are the two equations equal

Thu 9 Feb, 2012 01:58 pm
Math, Mathematics, Algebra, Formulas

Here are the basic problem parts:
1) SP - DP(1) +FF = 4Req
2) E + DP(2) = Cur

Examples:
1) If SP = 500,000, DP(1) = 0, FF = 10,750
Req = 510,750 / 4 = 127,688

2) If E = 104,250, DP(2) = 0
Cur = 104,250

At what point will DP(1&2) be the same and Cur and Req also be the same rounded to the nearest whole number

If DP is increased by the difference between Cur and Req, the values are not accurate:
127,688 - 104,250 = 23,438

1) If SP = 500,000, DP(1) = 23,438, FF = 10,750
Req = (500,000-23,438+10,750) / 4 = 121,828

2) If E = 104,250, DP(2) = 23,438
Cur = 107,688

Ideally, 18,750 should be the result.

I tried substituting Cur for Req as the should be equal to each other, but I get the following
1) SP - DP(1) +FF = 4Req
2) E + DP(2) = Cur

500,000-DP(1) +10,750 = 4 (104,250 + DP(2))
125,000-.25(DP(1)) +2,687.50 = 104,250 + DP(2)
125,000-104250+2,687.50 = .25(DP(1)) + DP(2)
18,062.50 = 1.25DP - as DP(1) and DP(2) should be the same
18,062.50 / 1.25 = DP = 14,450

Any ideas?
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engineer

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Thu 9 Feb, 2012 02:22 pm
@goofy78270,
You have two equations in seven variables. Even if you restrict two of them by setting them equal, you have two equations in five variables. That's not going to have a unique solution. If you set DP(1)=DP(2) and Cur=Req you can restate everything to:

SP - DP + FF = 4(E + DP)
SP + FF - 4E = 5DP

Pick any value you want for three of those variables and compute the fourth.
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