Lesson 2 · from §35 of the 1910 text
Binomials as Quantities
In word problems, a quantity is often a binomial like x - 4 or b + 10. Treat it as a single number by wrapping it in parentheses.
- A rectangle x - 4 long and 3 wide has area 3(x - 4) = 3x - 12.
- x horses at b + 10 dollars each cost x(b + 10) dollars.
- Percent means hundredths: 5% of x is \tfrac{5}{100}x = 0.05x.
Quick check
What is 6% of x? (Answer as an expression.)
Exercises
How to type math
Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.
Represent each quantity.
The length of a rectangle is a and its breadth is b. What is its area? its perimeter?
The length of a rectangle is x - 4 and its width is 3. What is its area? its perimeter?
What is the area of a rectangle whose length is 2x - 4 and whose breadth is x + 2? the perimeter?
Each of four horses cost $100. What was the cost of all, in dollars?
Each of n horses cost $80. What represents the cost of all, in dollars?
Each of a books cost b cents. What represents the cost of all, in cents?
What is the total cost of x hats at a cents each and y hats at b cents each?
What is the cost of x horses at b + 10 dollars each?
Represent the total cost of x chairs at b + 2 dollars each and y chairs at c - 3 dollars each.
What is 5% of 16? of x?
What is 3% of x + 120? of 12x - 300a?
A is n years old. What will three times his age 4 years from now be?
Two sums of money are x dollars and 1000 - x dollars. Express as equations: (a) 4% of the first sum equals $180. (b) 3% of the first equals 5% of the second. (c) 5% of the first is $20 less than 4% of the second.
A picture is 10 inches wide and 12 inches long and has a frame 2 inches wide. What are the outside dimensions of the frame?
If the frame in Exercise 14 were x inches wide, what would represent the outside width and length of the frame? the area of picture and frame together? the area of the picture? the area of the frame alone?