Finding A Mathematical Model...2

[nycmathguy]

Section 1.10
62 & 64

62. The simple interest on an investment is directly proportional to the amount of the investment. An investment of $6500 earns $211.25 after 1 year. Find a mathematical model that gives the interest I after 1 year in terms of the amount invested P.

Let me see what I can do here.

Let I = interest
Let k = constant of proportionality
Let P = investment

Using the above information, I get I = kP as the general form of an equation in terms of interest.
I think I need to find k.

211.25 = 6500k

211.25 ÷ 6500 = k

0.0325 = k

I = (0.0325)P

Correct?

64. Use the fact that 14 gallons is
approximately the same amount as 53 liters to find a mathematical model that relates liters y to gallons x. Then use the model to find the numbers of liters in 5 gallons and 25 gallons.

Let me see.

Let x = 14, when y is 53. I need to find k.

y = kx

53 = 14k

53/14 = k

The mathematical model is y = (53/14)x.

Let x = 5 gallons.

y = (53/14)(5)

y = 18.9285714285

I will round off to the units place to get 19 liters.

Let x = 25 gallons.

y = (53/14)(25)

y = 94.6428571425

I will round off to the units place to get 95 liters.

You say?

 

[MathLover1]

Correct

 

[nycmathguy]

Correct

It feels so good to solve word problems. I think there is no greater skill in mathematics than solving word problems. Do you know how many city job exams I failed throughout my life due to lack of skills solving word problems?

 

[MathLover1]

word problems are math applied in real life

Math Matters in Everyday Life

• Managing money $$$
• Balancing the checkbook.
• Shopping for the best price.
• Preparing food.
• Figuring out distance, time and cost for travel.
• Understanding loans for cars, trucks, homes, schooling or other purposes.
• Understanding sports (being a player and team statistics)
• Playing music.
• and so on

 

[nycmathguy]

word problems are math applied in real life

Math Matters in Everyday Life

• Managing money $$$
• Balancing the checkbook.
• Shopping for the best price.
• Preparing food.
• Figuring out distance, time and cost for travel.
• Understanding loans for cars, trucks, homes, schooling or other purposes.
• Understanding sports (being a player and team statistics)
• Playing music.
• and so on

By the way, I read and write guitar tablature at an intermediate level. I play hymns using the firgerstyle method. I started playing guitar in the early 1970s. I sold my last guitar in 2018. Needed the money to move from one area in the Bronx to another area in the same borough.

 

[MathLover1]

cool

 

[nycmathguy]

cool

Thanks.