Problem: 1.7f + 1.3s+37.9 and 5.6f + 5.4s=147.2
trying to solve( 1.7f +1.3s=37.9)
and ( 5.6f +5.4s=147.2)
This is a system of two equations in two unknowns. There
is a specific process for handling these problems.
1.7f + 1.3s = 37.9
5.6f + 5.4s = 147.2
Let's eliminate all the decimal values by multiplying
everything by 10.
1) 17f + 13s = 379
2) 56f + 54s = 1472
The first thing we want to do is eliminate one of
the unknowns, either the f or the s. We do that by
getting the co-efficients in both equations to the
same value for one of the unknowns. It would be great
if the co-efficient in one equation were a multiple of
the co-efficient in the other equation, but that isn't
the case here. So, let's choose to eliminate the s by
multiplying equation 1 by 54 and multiplying equation
2 by 13.
54 * (17f + 13s) = 379 * 54
3) 918f + 702s = 20466
13 * (56f + 54s) = 1472 * 13
4) 728f + 702s = 19136
This allows us to subtract equation 4 from equation 3.
918f + 702s = 20466
-(728f + 702s = 19136)
----------------------------
190f = 1330
190f = 1330
190f/190 = 1330/190
f = 7
We use that value for f in one of the original equations
to solve for s. Use equation 1.
17f + 13s = 379
17(7) + 13s = 379
119 + 13s = 379
119 + 13s - 119 = 379 - 119
13s = 260
13s/13 = 260/13
s = 20
We verify both values by using them in the other equation.
56f + 54s = 1472
56(7) + 54(20) = 1472
392 + 1080 = 1472
1472 = 1472
Answer: f = 7, s = 20