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**