251. Find a simple method of solving:

6751X + 3249Y = 26751

3249X + 6751Y = 23249

Add the equation to give: 10000X + 10000Y = 50000

Divide by 10000 to give: X + Y = 5

Subtract to give: 3502X - 3502Y = 3502

Divide by 3502 to give: X - Y = 1

Therefore: X = 3 and Y = 2.

252. Two friends decide to get together; so they start riding bikes towards each other. They plan to meet
halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant
the friends start traveling. The pigeon flies back and forth at 18 MPH between the 2 friends until the friends meet. How far does the pigeon travel

It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 18 MPH = 54 miles.

253. Nick and John were exercising when the subject of weight came up. Nick had no problem telling John his
weight, but John said he had more "mass" than he wanted. He wouldn't come right out and reveal his weight; so he told Nick this
riddle. " I weigh 147 pounds plus half of my weight," he said. How much does he weigh?

If John weighs 147 pounds plus half of his body weight, the 147 pounds represents the other half. John weighs 294 pounds.

254. A farmer knows that 20 of his hens, housed in 3 coops, will hatch 30 eggs in 18 days. How long will it take
30 hens, housed in 4 coops to hatch the same number of eggs?

You can't shorten the process of egg-hatching by increasing the number of chickens. Therefore, 30 hens will also need 18 days to hatch their eggs.

255. How can you measure 1 gallon of juice out of a barrel, if all you have available is a 3-gallon and a 5-gallon pitcher?

Fill the 3 gallon pitcher and pour it into the 5 gallon pitcher. Now fill the 3 gallon pitcher again and fill the 5
gallon pitcher to capacity. What remains in the 3 gallon pitcher is one gallon of juice.

256. Students at Monty High with a class size under of 30 took a math test. One third of the class got a "B",
one quarter a "B-", one sixth a "C", and one eighth failed. The remainder of the students got an "A" How many students got an "A"?

First find the common denominator for the numbers 3, 4, 6, and 8. The only common denominator less than 30 is 24.
Therefore, the students with a "B" = 8, "B-" = 6, "C" =4, failed = 3. This represents 21 of the students; so the 3
remaining students received an "A".

257. When manufacturing bars of soap, the cutting machine produces scraps. The scraps from 11 bars of soap
can be made into one extra bar. What is the total number of bars that can be made after cutting 250 bars of soap?

Divide 250 by 11 which equals 22.8. Now when you combine the extra 8 scraps with the scraps you'll have from the 22 bars,
you'll have 30 more scraps. They will produce 2 more bars; so the total additional bars will be 24.

258. Kerry loves dumplings. He can eat 32 of them in an hour. His brother Pete needs 3 hours to eat the same
amount. How long will it take them both together to eat 32 dumplings?

If Kerry eats 3 times as fast as Pete, he must be able to eat 3 times as many dumplings as his brother. Therefore, Kerry eats 24
while Pete eats 8 ( 32 ÷ 4 = 8 ). Together it takes them 45 minutes.

259. Joe bought a bag of oranges on Monday, and ate a third of them. On Tuesday he ate half of the remaining
oranges. On Wednesday he looked in the bag to find he only had two oranges left. How many oranges were originally in the bag?

He had 6 oranges to start with, and ate 2 the first day and 2 the second day.

260. Joan and Jane are sisters. Jean is Joan's daughter and 12 years younger than her aunt. Joan is twice
as old as Jean. Four years ago, Joan was the same age as Jane is now, and Jane was twice as old as her niece. How old is Jean?

Joan is 32, Jane is 28, and Jean is 16.