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

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Solution M = V; Curly = X; Larry = XX

Another Taxi Story

In the Twin Cities, taxi fare works like this: as soon as the passenger gets in, the driver drops the flag and $2.50 appears on the meter. Every mile, including the first mile, costs an additional $1.90. Fractions of a mile are 38 cents for every 1/5 of a mile.

My car wouldn't start and I needed to take an urgent trip. Using Mapquest, I found the trip was 15.6 miles long. What was the likely fare, including a 20% tip? Round the fare plus tip to the nearest dime (10 cents).

I found out in advance that the taxi company accepts credit cards. But, if not, could I have paid with $40 in cash?

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Answer: XXXVIII dollars and LX cents. I could have paid with two twenty-dollar bills.

Note: V=5, X=10, and L=50.