Real-Life Math -- Solution
1. This is an exercise in logic and there are 2 solutions:
I
have 3 flowers -- rose, tulip, daisy
I have 2 flowers -- carnation,
geranium
Think about this: imagine the flowers, how they look and smell,
how they feel in your hand. Even better, make a picture of each flower and
hold them in your hand. When you use the word "except," cover the flower or
flowers that you are excluding. The logic here is that all can mean 1 as well
as more than 1. Except can mean the exclusion of 1 or the exclusion of all.
2.
This is another exercise in logic:
Each person paid $17,
totalling $51. The cashier has $50 and the server has $1.
The server's
$1 should be added to the cashier's $50 or subtracted from the customers'
$51, not added to the customers' $51.
Here our thinking was confused.
We incorrectly added the $1 to the customers' $51.
(1 + 51) = 52
and the difference between the original: $60 and $52 = $8
(So that's
where we came up with $8! The math was OK but the logic was wrong!)
The
difference (60 - 51 = $9) was returned to the 3 customers at $3 each.
3.
The solution here is a matter of analyzing this problem. What are the things
we know about this problem? Take it apart and analyze it.
We
know that time is involved. We know that distance is involved. We know that
speed or velocity (miles per hour) is involved. So, we have time (T), distance
(D), and speed or velocity (V).
We know the formula to calculate distance
is: Distance = Velocity x Time. We know that we can invert (switch it around,
back to front) the formula, like this:
IF:
D = VT
THEN: T = D / V
AND THEREFORE: V = D / T
What
do we want to know in this particular problem? Velocity! How fast is this
plane traveling?
V = n (the unknown factor)
D
= 168 miles
T = (10:43 - 10:30) = 13 min.
V = D / T
V = 168
miles / 13 minutes
V = 12.923 miles in 1 minute
V = (12.923 miles
per minute x 60 minutes per hour) = 775.38 miles in 1 hour
The plane
was traveling at 775.38 miles per hour.
By analyzing this
problem, taking it apart into its various components, we can more clearly
see what is needed to solve the puzzle.