I am not seeing a picture so I am going to give you the instructions to do it yourself. All you would have to do is divide the total perimeter (35 centimeters) by however many sides the polygon has. For example, if it was a pentagon, then the equation would be 35/5, which would equal 7.
Notice the tickmarks on the graph, those two sides are equal, and those two angles are also equal, now, the (4x-10) side, is shared by both triangles above and below.
namely the triangles above and below have a [S]ide and then an [A]ngle and then a [S]ide in common, thus they're congruent by SAS.
what does that mean? well, it means that 8x-2 = 3x - 5, and you know the rest then.
though for some reason you put a line through the -, to make it 3x+5, so, dunno what it might be, but those sides are congruent either way.
Let x represent the gallons of water that is 10% salt.
Let y represent the gallons of water that is 25% salt.
Now, write the system of equations:
x + y = 10
.10x +.25y = 0.20 • 10
1) To make the system easier to solve, multiply all the terms in .10x +.25y = 0.20(10) by 100 to make them integers.
10x + 25y = 20 • 10
10x + 25y = 200
2) Solve for x.
x + y = 10
x = 10 - y
3) Substitute x with 10 - y in the other equation.
10(10 - y) + 25y = 200
100 - 10y + 25y = 200
Combine like terms.
100 + 15y = 200
Subtract 100 from both sides.
15y = 100
y = 20/3 or 6 2/3
4) Now that we have the numerical value of y, solve for the value of x by substituting once more.
a) x + y = 10
x + 20/3 = 10 or x + 6 2/3 = 10 (either equation is fine)
x = 10/3 or x = 3 1/3
The manager should combine 3 1/3 (3.33) gallons of 10% salt water and 6 2/3 (6.67) gallons of 25% salt water.
5) Always check the answers to make sure.
a) x + y = 10
3 1/3 + 6 2/3 = 10
9 3/3 = 10
10 = 10
b) .10x +.25y = 0.20 • 10
.10(3 1/3) +.25(6 2/3) = 0.20 • 10
1/3 + 5/3 = 2
6/3 = 2
2 = 2
