Page 17 - How To Solve Word Problems In Calculus

Number Problems
Although number problems are relatively simple, they illus-
trate the above steps quite clearly.

EXAMPLE 3
The sum of two numbers is 40. Express their product as a func-
tion of one of the numbers.

Solution
Step1
In most number problems a diagram is not called for. We
label the numbers using the variables x and y.
Let x be the first number
y be the second number
Step2
We wish to express the product P as a function, so P = xy.
Step3
Since x + y = 40, y = 40 − x. We substitute into the equa-
tion involving P obtained in step 2 and express using function
notation.

P(x) = x(40 − x)
P(x) = 40x − x 2

EXAMPLE 4
The product of two numbers is 32. Find a function that repre-
sents the sum of their squares.

Solution
Step1
Let x be the first number and y the second.
Step2
2
S = x + y 2
Step3
2
32 32
2
Since xy = 32, y = . It follows that S(x) = x + .
x x
4