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Four More Math Puzzles

Here are a few more math puzzles to exercise that brain.

1. Look at the following:

1 + 23 - 4 + 5 - 6 + 78 + 9 = 106

Notice that the digits 1 through 9 are used in order to arrive at 106. Using 1 through 9 in order, and using only addition or subtraction, create an equation that equals 100.

2. Mary is 54 years old, and her mother is 80. How many years ago was her mother three times the age of her daughter Mary?

3. John needed some small bills because he was traveling. He went into a bank and gave the teller a $100 bill. He told her, "I need some two-dollar bills, ten times as many one-dollar bills, and the rest in five-dollar bills. How many of each did the teller give him?

4. Bob makes and sells picnic tables from his yard for $100 each. His only costs are for materials. It takes him an hour and half to make a table. He sold 200 last year, for a profit of $3,000. This year he raises the price by 15%, but sells 30% fewer tables. Assuming his cost for making each table hasn't changed, by what percentage does his profit increase?

Solutions

1. 12+3-4+5+67+8+9 = 100. But that's just one solution. "Fuzz" sent me this one: 123+45-67+8-9 = 100.) Here are some Vipul sent (thank you):
1+2+3-4+5+6+78+9=100
1+2+34-5+67-8+9=100
1+23-4+5+6+78-9=100
1+23-4+56+7+8+9=100
12+3+4+5-6-7+89=100
12-3-4+5-6+7+89=100
123+4-5+67-89=100
123-4-5-6-7+8-9=100
123-45-67+89=100

2. 41 years ago, when Mary was 13 and her mother was 39.

3. He was given five two-dollar bills, fifty one-dollar bills, and eight five-dollar bills, totaling $100.

4. 40%. This is a good business math puzzle, with a lesson or two in it. His profit on 200 tables was $3,000, or $15 per table, so we can deduce that his cost is $85 per table. At the new price of $115 (15% more) he makes $30 per table. Thus, even though he sells only 140 tables (30% fewer), he makes $4,200 - 40% more than the previous year.

Interestingly, a 15% price increase makes his profit per-hour-of-labor go up 100%, from $10 per hour to $20 per hour - showing the importance of selecting the right price.

Note: You can find more on the page: Math Puzzles.


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