Concentrate: Water: Orange Juice
1: 3: 4
C:W:(200 x 6)

C = 200 x 6/4 = 300

300/12 = 25

BDC and AEC are similar triangles.
AE is 40 and BD is 5, so the larger triangle is 8 times the area of the smaller one.
The area of BDC is 5 x 10/2 = 25
Therefore AEC has area 25 x 8 = 200
200-25 = 175
Answer A

Remember rate questions use reciprocals:
A's rate = 1/6
B's rate = 1/12
Joint rate = 1/6 + 1/12 = 1/4
2 days at 1/4 = 2 x 1/4 = 1/2 -> job is half complete
A's new rate = 0.75 x 1/6 = 1/8 to do the other half of the job
so A will take 8/2 = 4 days

Alternatively, we can see that a SUBTRACTION is required, so we can use this clue to bring us closer to the answer on the right hand side of the equation:
3 x 2^13 = (4-1) x 2^13 = 4 x 2^13 - 2^13 = 2^15 - 2^13 = 2^n - 2^(n-2)
So n = 15

Upon visualising the given coordinates it is easy (and fast) to realise that the triangle is symmetrical about the line y = -x. Therefore, if the x co-ordinate of the third vertx is 6, then the y co-ordinate must be -6.
No need for any trig or Pythagoras.

In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle? The displacement between points (2,-3) and (5,0) is the radius of the circle. Change in x = 5 - 2 = 3 Change in y = 0 - -3 = 3 By Pythagoras: r^2 = 3^2 + 3^2 = 18 Area = pi x r^2...

Here's a another way of working backwards from the answers. Answers changed to reflect manufacturing just w widgets: A. x = 2, y = 0: 1/2 + 1/0 = UNDEFINED B. x = 3, y = 1: 1/3 + 1/1 = 4/3 in 1 day, so 4 in 3 days C. x = 4, y = 2: 1/4 + 1/2 = 3/4 in 1 day, so 9/4 in 3 days D. x = 5, y = 3: 1/5 + 1/...

So, 12(x -2) + 12x = 5x(x-2) Rearrange to make a quadratic: 5x^2 - 34x + 24 = 0 (5x-4)(x-6) = 0 x = 4 or 6 As X takes 2 days longer than Y, then x = 6, y = 4 to make w widgets Therefore, 2w widgets take X 12 days to make. The highlighted step should be x = 4/5 or 6 Well spotted... oops! Thanks for ...