DAY 419
Together, a hat and scarf cost $11.00. The hat costs $2.00 more than the scarf. What is the price of each?
Answer:
$6.50 for the hat and $4.50 for the scarf.........This counter-intuitive answer can be found by trial and error or algebra [x + (x + 2) = 11]. But a more interesting way to solve the problem is to divide $11.00 in half - $5.50 - and "splitting the difference" of $2.00 by going up $1.00 and down $1.00 - giving $6.50 and $4.50.
NOTE: See also DAY 57 - "bottle and cork" problem
Similar Problem:
Together, soup and a sandwich cost $3.50. A sandwich costs $1.00 more than soup. What is the price of each?
Answer:
$2.25 for the sandwich and $1.25 for the soup
Monday 30 December 2013
Monday 25 November 2013
Tuesday 19 November 2013
DAY 417
Fill in the blanks with five different numbers so that the following makes sense when read aloud:
We had been on a losing streak _____ much _____ long. But today we finally _____ a game. To celebrate we _____ _____.
Answer:
We had been on a losing streak 4 much 2 long. But today we finally 1 a game. To celebrate we 8 (Pi).
Credit: GAMES Magazine - April, 2006
R. H. Wei
EASY AS PIE
Fill in the blanks with five different numbers so that the following makes sense when read aloud:
We had been on a losing streak _____ much _____ long. But today we finally _____ a game. To celebrate we _____ _____.
Answer:
We had been on a losing streak 4 much 2 long. But today we finally 1 a game. To celebrate we 8 (Pi).
Credit: GAMES Magazine - April, 2006
R. H. Wei
EASY AS PIE
Sunday 17 November 2013
Sunday 6 October 2013
DAY 415
Doofus and Goofus were playing a game in which the winner won $1.00 for each victory. In the end, Doofus won $7 and Goofus won 7 games. How many games were played?
Answer:
21 ........... If Doofus won $7, he must have won 7 more games than Goofus. If Goofus won seven games, Doofus must have won 14 games. 14 + 7 = 21.
Doofus and Goofus were playing a game in which the winner won $1.00 for each victory. In the end, Doofus won $7 and Goofus won 7 games. How many games were played?
Answer:
21 ........... If Doofus won $7, he must have won 7 more games than Goofus. If Goofus won seven games, Doofus must have won 14 games. 14 + 7 = 21.
Tuesday 30 July 2013
Sunday 21 July 2013
DAY 413
Credit: NPR Car Talk Puzzler
June 29, 2013
Tom and Ray, the Car Talk brothers, go out to eat with a group of friends. When the bill comes, the two brothers go to the bathroom and climb out the window. Realizing they've been stiffed, the remaining group looks at the bill, which is $63. One of them correctly says, "If each of us chips in an extra two dollars, we'll have it covered." How many were in the original group (i.e. including Tom and Ray)?
Answer:
Nine ............. The only two factors of 63 with a difference of two are 7 and 9. If Tom and Ray had paid their share, each of the nine people would have paid $7. Now, each of the remaining
seven people have to pay $9 each - a difference of $2.
Credit: NPR Car Talk Puzzler
June 29, 2013
Tom and Ray, the Car Talk brothers, go out to eat with a group of friends. When the bill comes, the two brothers go to the bathroom and climb out the window. Realizing they've been stiffed, the remaining group looks at the bill, which is $63. One of them correctly says, "If each of us chips in an extra two dollars, we'll have it covered." How many were in the original group (i.e. including Tom and Ray)?
Answer:
Nine ............. The only two factors of 63 with a difference of two are 7 and 9. If Tom and Ray had paid their share, each of the nine people would have paid $7. Now, each of the remaining
seven people have to pay $9 each - a difference of $2.
Saturday 20 July 2013
DAY 412
A fruit seller has a basket of oranges. His first customer buys half the oranges plus half an orange. The next customer buys half of what's left plus half an orange. The last customer buys half of what's left plus half an orange, leaving the basket empty. No oranges were cut or broken in any way. How many oranges did the fruit seller start with?
Answer:
Problems like these can be solved with algebra, but a simpler solution is possible. Since the problem tells us no oranges were cut or broken, we know that only whole oranges were sold to the customers. The "half" orange must be used to complete a whole orange - as in 1 1/2 + 1/2 = 2. The only way to take half of a number and add 1/2 to it to get a whole number, is to start with an odd number.
In this problem, since there were only three transactions before the basket was emptied, there could not have been that many oranges. Thinking of the odd numbers - 1, 3, 5, 7, 9, 11 ............... 7 oranges solves the problem:
First customer: 3 1/2 (half of seven) + 1/2 = 4 (leaving 3)
Second customer: 1 1/2 (half of three) + 1/2 = 2 (leaving 1)
Third customer: 1/2 (half of one) + 1/2 = 1 (leaving 0)
A fruit seller has a basket of oranges. His first customer buys half the oranges plus half an orange. The next customer buys half of what's left plus half an orange. The last customer buys half of what's left plus half an orange, leaving the basket empty. No oranges were cut or broken in any way. How many oranges did the fruit seller start with?
Answer:
Problems like these can be solved with algebra, but a simpler solution is possible. Since the problem tells us no oranges were cut or broken, we know that only whole oranges were sold to the customers. The "half" orange must be used to complete a whole orange - as in 1 1/2 + 1/2 = 2. The only way to take half of a number and add 1/2 to it to get a whole number, is to start with an odd number.
In this problem, since there were only three transactions before the basket was emptied, there could not have been that many oranges. Thinking of the odd numbers - 1, 3, 5, 7, 9, 11 ............... 7 oranges solves the problem:
First customer: 3 1/2 (half of seven) + 1/2 = 4 (leaving 3)
Second customer: 1 1/2 (half of three) + 1/2 = 2 (leaving 1)
Third customer: 1/2 (half of one) + 1/2 = 1 (leaving 0)
DAY 411
Instead of buying 4 hamburgers and 3 drinks for $14.50, Ralph buys 3 hamburgers and 4 drinks for $13.50. What is the price of each hamburger and each drink?
Answer:
Each hamburger is $2.50 and each drink is $1.50.
7 hamburgers and 7 drinks would cost $28.00.
1 hamburger and 1 drink cost $28.00/7 = $4.00.
Instead of buying 4 hamburgers and 3 drinks for $14.50, Ralph buys 3 hamburgers and 4 drinks for $13.50. What is the price of each hamburger and each drink?
Answer:
Each hamburger is $2.50 and each drink is $1.50.
7 hamburgers and 7 drinks would cost $28.00.
1 hamburger and 1 drink cost $28.00/7 = $4.00.
Sunday 14 July 2013
Subscribe to:
Posts (Atom)