MATH Destroyer Test #8 Question #5:

If it takes "a" pounds of grain to feed "b" pigs, how many pounds of grain will it take to feed "c" pigs?

Can somebody give me a logical answer to this?

One of the powerful ways to solve a problem is to change the problem and find the logic behind it.

#5

If it takes "1" pounds of grain to feed "2" pigs, how many pounds of grain will it take to feed "3" pigs?

The answer is 1.5. Easy enough? But how did I come up with 1.5 is the question. Well I can say 1 pound feed 2 pigs, so 0.5 lb feed 1 pig and since there are 3 pigs, 0.5x3 = 1.5 lbs. Or everything in one step: 3 pigs*1 lb/2 pigs = 1.5 lbs.

So If it takes "a" pounds of grain to feed "b" pigs, how many pounds of grain will it take to feed "c" pigs?

The answer is c*a/b lbs!

#7 A bicyclist travels 56 miles to a Trading Post at a constant speed. On his return trip he travels at half the speed. If the round trip takes 6 hours, what is his speed on the way to the Trading Post?

Lets assign some variables

Time/velocity for first trip: t1, v1

Time/velocity for second trip: t2, v2

first trip = constant speed and second trip = half speed

These tell you the time he takes for his second trip is twice as much as the first trip or t2 = 2t1

The round trip takes 6 hours or t1 + t2 = 6

Solving for t1 = 2 hours

v1 = d1/t1 = 56/2 = 28 miles/hr