Could somone help me with some math?

Question

I just need explanations of these problems.

1. Two greyhounds are casing a rabbit that has a 90 rabbit-jump start. While the rabbit jumps 10, the greyhounds jumps 7, but the length of two jumps of the greyhound equals the length of 5 rabbit- jumps. In how many jumps do the greyhounds catch the rabbit?

2. The price of 10 pounds of apples is d dollars. If the apple weighs an average 1 pounds for every 6 apples, which of the following is the average price, in cents, of a dozen such apples?
A) 20d
B) (50d)/3
C) 5d
D) (5d)/3
E) d/20

3. To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of green and orange dye are mixed, what is the proportion of yellow bye in the new mixture?
A) 3/16
B) 1/4
C)11/30
D) 3/8
E) 7/12

Answer 1

(1)
Rabbit distance = 90 + 10t
Dog distance = 7t * (5/2)

5/2 is the conversion from dog-jumps to rabbit-jumps. The two meet when the distances are equal:

90 + 10t = 7t * (5/2)
180 + 20t = 35t
180 = 15t
t = 12 (units of 10 or 7 jumps)

12 * 10 jumps = 120 rabbit jumps.
12 * 7 jumps = 84 greyhound jumps.

Just to check: The rabbit makes 120 jumps plus its 90-jump head-start, for 210 total rabbit-jumps from where the dogs start. 210 * (2/5) = 84, converting to dog-jumps.

(2) Apples are d/10 dollars per pound. If six apples weight one pound, a dozen weigh two pounds. Two pounds would cost 2*d/10 dollars, which is d/5.

d/5 * 100 (cents per dollar) = 20d cents per pound.

(3) yellow die is 2/(2+3) = 2/5 of orange, and 1/(1+2) = 1/3 of green. If equal amounts are mixed, you'd add (1/2 * 2/5) + (1/2 * 1/3) yellow die, which is 1/5 + 1/6.

1/5 + 1/6 =
6/30 + 5/30 =
11/30