Dear ZaireMcfalane33, if you subtract with fraction strips the answer will be smaller, but if you add with fraction strips the answer will be bigger.
Loosely, "varies inversely" means that as one quantity increases, the other decreases. Specifically, if x and y vary inversely, then y = k/x where k is some constant (a particular number).
Another way to write that relationship is xy = k. To find the value of k for this problem, you need a numbers for x and y that go together.
Suppose x = number of children and y = number of candies (it doesn't matter what order these go in as long as you keep track!).
"When 12 children are present, 140 pieces of candy are consumed." So when x = 12, the value of y = 140.
xy = k
(12)(140) = k
1680 = k
Now, when x = 8 children,
8y = 1680
y = 210
Cos(x°) = (√3)/2
cos⁻¹[(√3)/2] = x°, that means x° = 30°
The two triangles are similar and equal therefore; It means the corresponding sides are equal and the corresponding angles are equal. Hence;
ZX=EF, thus,ZX = 1.3 in.
EG = XY, thus, EG = 3.0 in.
m∠ X = m∠E, thus m ∠X = 48°
m∠ G = m∠Y, and angles in a triangle add up to 180 thus;
m ∠ G=180- (107 +48) = 25°
