Arecipe requires 3/4 cup of nuts for one cake.
enter the maximum number of cakes that can be made using seven and a half cups of nuts. how many cakes can be made with 7 1/2 cups of nuts?

10. How I would solve it, is I would convert them into decimals so it is 7.5/.75.

29 cakes 
work below 
3/4 x 2 = 1/2 cups 
3/4 x 4 = 1 cups 
3/4 x 28 = 7 cups 
+ 2 3/4 cups = 29 = 7 1/2 cups 
29 cakes can be made 

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12