This morning, I walked 2.4 miles in 34.5 minutes. What was my walking speed in miles per hour?
Round your answer to nearest tenth.
Hint: Convert 34.5 minutes to fractional hour by dividing by 60 (60 minutes per hour). For example, 30 minutes is 0.5 hour.
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Answer: faster than IV MPH, not as fast as V MPH.
Wednesday, May 21, 2008
The $600 Economic Incentive Payment
The Federal Government is sending many taxpayers a $600 check to boost the economy (May, 2008).
One writer, who drives a 1984 Volvo station wagon that gets 18 miles to the gallon, thought about spending the money for gasoline. He lives near San Francisco, CA, where gasoline is very expensive. He pays $4.19 for one gallon. All taxes are included in that $4.19.
To the nearest gallon, how many gallons could he buy?
To the nearest mile, how many miles could he drive with that gasoline?
Just for fun, can you find someplace he can drive to, and return, from San Francisco with that much gasoline?
Answer here:
One writer, who drives a 1984 Volvo station wagon that gets 18 miles to the gallon, thought about spending the money for gasoline. He lives near San Francisco, CA, where gasoline is very expensive. He pays $4.19 for one gallon. All taxes are included in that $4.19.
To the nearest gallon, how many gallons could he buy?
To the nearest mile, how many miles could he drive with that gasoline?
Just for fun, can you find someplace he can drive to, and return, from San Francisco with that much gasoline?
Answer here:
Tuesday, May 20, 2008
Word Problems: Hands-on Equations
At Seward Elementary, a public elementary school in Minneapolis MN, a substantial number of 3rd-grade and 4th-grade students are doing linear algebra using the Hands-On Equations method of Henry Borenson, Ed.D.
Lately, we have been doing word problems. Here is a link to Dr. Borenson's site with 11 verbal problems; after you get there, click on Verbal Problems at the top of the page: click here:
In accordance with our theme of money problems, I repeat #11 here:
Curly, Larry and Moe each have a collection of silver dollars. Curly has 5 more coins than Moe, and Larry has double the number of coins that Curly has. The sum of the number of silver dollars in the entire collection is 35. How many coins did each person have? Extra credit: who were Curly, Larry and Moe?
In Borenson's pictorial notation:
Moe M
Curly M + 5
Larry M + 5 M + 5
35
==================
Solution M = V; Curly = X; Larry = XX
Lately, we have been doing word problems. Here is a link to Dr. Borenson's site with 11 verbal problems; after you get there, click on Verbal Problems at the top of the page: click here:
In accordance with our theme of money problems, I repeat #11 here:
Curly, Larry and Moe each have a collection of silver dollars. Curly has 5 more coins than Moe, and Larry has double the number of coins that Curly has. The sum of the number of silver dollars in the entire collection is 35. How many coins did each person have? Extra credit: who were Curly, Larry and Moe?
In Borenson's pictorial notation:
Moe M
Curly M + 5
Larry M + 5 M + 5
35
==================
Solution M = V; Curly = X; Larry = XX
Thursday, May 15, 2008
Unit Price: AA Alkaline Cells
The unit price is the price for one item. You find it by division and, perhaps, rounding.
Seward uses quantities of AA "batteries" to power graphing calculators. Strictly speaking, a single AA "battery" is a cell, 4 of them together form a battery. Today, at Home Depot, Energizer brand AA cells are for sale at the following prices:
36 cells for $12.89
20 cells for $10.47
10 cells for $6.87
6 cells for $4.77
Assuming you can use all the cells you buy, what is the price per cell, the unit price, for each package? Round results to the nearest cent.
==========
A note on standard tests. Standard tests often present a set of prices like the cell prices, and ask: "What is the lowest price per unit?" Often, but not always, the largest quantity has the lowest unit price. You should calculate all the unit prices, then pick the lowest one. Guessing is not a good idea. It isn't obvious, but the typical unit price problem requires four divisions, not much work if you have a calculator.
========
Answers: 36 pack, XXXVI cents per cell, 20 pack, LII cents per cell, 10 pack, LXIX cents per cell, 6 pack, LXXX cents per cell.
L= 50, X = 10, V = 5.
Seward uses quantities of AA "batteries" to power graphing calculators. Strictly speaking, a single AA "battery" is a cell, 4 of them together form a battery. Today, at Home Depot, Energizer brand AA cells are for sale at the following prices:
36 cells for $12.89
20 cells for $10.47
10 cells for $6.87
6 cells for $4.77
Assuming you can use all the cells you buy, what is the price per cell, the unit price, for each package? Round results to the nearest cent.
==========
A note on standard tests. Standard tests often present a set of prices like the cell prices, and ask: "What is the lowest price per unit?" Often, but not always, the largest quantity has the lowest unit price. You should calculate all the unit prices, then pick the lowest one. Guessing is not a good idea. It isn't obvious, but the typical unit price problem requires four divisions, not much work if you have a calculator.
========
Answers: 36 pack, XXXVI cents per cell, 20 pack, LII cents per cell, 10 pack, LXIX cents per cell, 6 pack, LXXX cents per cell.
L= 50, X = 10, V = 5.
Wednesday, May 14, 2008
Deep Discounts in a "Dollar Store"
In the United States, there are "dollar stores." Everything in these stores has a price of one dollar.
Teachers often go to these stores to buy extra school supplies for their students.
For example, a store might sell rulers in a package of 3 for one dollar.
You should beware of really deep discounts, but I saw a sign in a dollar store that was closing: "Everything must go, 75% off!"
So, I bought 4 packages of rulers, indeed the checkout clerk applied the 75% discount to each package, multiplied the discounted price by 4, and added 6.5% sales tax. The rulers were perfectly usable in school: they have centimeters and millimeters on one edge and inches on the other.
To the nearest cent, what was the price of one ruler?
=============
Answer: IX cents each. Alas, went I returned to the store to buy more, it was closed forever.
Teachers often go to these stores to buy extra school supplies for their students.
For example, a store might sell rulers in a package of 3 for one dollar.
You should beware of really deep discounts, but I saw a sign in a dollar store that was closing: "Everything must go, 75% off!"
So, I bought 4 packages of rulers, indeed the checkout clerk applied the 75% discount to each package, multiplied the discounted price by 4, and added 6.5% sales tax. The rulers were perfectly usable in school: they have centimeters and millimeters on one edge and inches on the other.
To the nearest cent, what was the price of one ruler?
=============
Answer: IX cents each. Alas, went I returned to the store to buy more, it was closed forever.
Monday, May 12, 2008
A Cab ride in Chicago with a Friend
Cab fares in Chicago work like this: when the ride starts, the driver drops the flag on the meter. An immediate charge of $2.25 appears. This charge covers the first 1/9 of a mile. For each additional 1/9 of a mile, the meter adds 20 cents. Hence, for miles after the first, the charge is $1.80 per mile. (What is posted in the taxi is: "$2.25 flag drop, $1.80 each additional mile.")
There is a flat (doesn't depend on distance) "surcharge" for each additional passenger.
The distance from your hotel to The Art Institute of Chicago is 1.38 miles. You could walk that far in about 20 minutes, but it is raining and you decide to take a cab. You take your friend along (one additional passenge). What is the meter charge when you arrive?
Hints: for the first mile, you are charged $2.25 plus 20 cents for each of the remaining eight ninths of a mile. You can then convert 1/9, 2/9 etc. into decimals and find how many ninths you have been charged for when you reach 1.38 miles.
You must add the passenger surcharge to this.
------------------
Answer: V dollars and XLV cents.
Roman Numerals: V=5, L=50, X=10. XL is the same as X + X + X + X, or L minus X.
There is a flat (doesn't depend on distance) "surcharge" for each additional passenger.
The distance from your hotel to The Art Institute of Chicago is 1.38 miles. You could walk that far in about 20 minutes, but it is raining and you decide to take a cab. You take your friend along (one additional passenge). What is the meter charge when you arrive?
Hints: for the first mile, you are charged $2.25 plus 20 cents for each of the remaining eight ninths of a mile. You can then convert 1/9, 2/9 etc. into decimals and find how many ninths you have been charged for when you reach 1.38 miles.
You must add the passenger surcharge to this.
------------------
Answer: V dollars and XLV cents.
Roman Numerals: V=5, L=50, X=10. XL is the same as X + X + X + X, or L minus X.
A Cab ride in Chicago
Cab fares in Chicago work like this: when the ride starts, the driver drops the flag on the meter. An immediate charge of $2.25 appears. This charge covers the first 1/9 of a mile. For each additional 1/9 of a mile, the meter adds 20 cents. Hence, for miles after the first, the charge is $1.80 per mile. (What is posted in the taxi is: "$2.25 flag drop, $1.80 each additional mile.")
The distance from your hotel to The Art Institute of Chicago is 1.38 miles. You could walk that far in about 20 minutes, but it is raining and you decide to take a cab. What is the meter charge when you arrive?
Hints: for the first mile, you are charged $2.25 plus 20 cents for each of the remaining eight ninths of a mile. You can then convert 1/9, 2/9 etc. into decimals and find how many ninths you have been charged for when you reach 1.38 miles.
------------------
Answer: IV dollars and XLV cents.
The distance from your hotel to The Art Institute of Chicago is 1.38 miles. You could walk that far in about 20 minutes, but it is raining and you decide to take a cab. What is the meter charge when you arrive?
Hints: for the first mile, you are charged $2.25 plus 20 cents for each of the remaining eight ninths of a mile. You can then convert 1/9, 2/9 etc. into decimals and find how many ninths you have been charged for when you reach 1.38 miles.
------------------
Answer: IV dollars and XLV cents.
Friday, May 9, 2008
How Many Miles Per Year Do I Drive?
I first drove my car on August 30, 2006. I suspect that I drive less than 10 000 miles per year. I notified my insurance company of this and they reduced the price of my car insurance.
The insurance company advised me to check how many miles I drove from time to time.
On March 8, 2008 the car told me that I had driven 15 000 miles and I needed an oil change. About how many miles do I drive per year?
-----------------
Hints: this is an estimation problem. You could, for example, assume that a year has 12 months, each of 30 days, and even assume that the the 15 000 mile notice appeared on April 30, 2008. Then get the miles per month and multiply by 12 to get miles per year.
-----------------
One approximate answer: DCCL miles per month times XII.
The insurance company advised me to check how many miles I drove from time to time.
On March 8, 2008 the car told me that I had driven 15 000 miles and I needed an oil change. About how many miles do I drive per year?
-----------------
Hints: this is an estimation problem. You could, for example, assume that a year has 12 months, each of 30 days, and even assume that the the 15 000 mile notice appeared on April 30, 2008. Then get the miles per month and multiply by 12 to get miles per year.
-----------------
One approximate answer: DCCL miles per month times XII.
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