1
A, who weighs 100 pounds, balances B, who weighs 120 pounds. B is 80 inches from the fulcrum. How far from it is A? (Answer in feet.)
Chapter 17 · Equations Containing Fractions
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
0first-try
0of 10 done
From The Lever, exercise 2
Use l_1W_1 = l_2W_2. Give numbers only; the units are filled in.
From Problems Leading to Fractional Equations, exercise 11
2
Separate 112 into two parts such that their quotient is \frac92.
From Literal Equations, exercise 9
Solve for x. Type the root in terms of the other letters, like x = a + 2b or 3c/4.
3
\displaystyle \frac{x}{2a}=b
From Polynomial Denominators, exercise 20
Solve and check. A number that makes a denominator zero is not a root. If an equation has no root, type none. If it has two roots, separate them with a comma.
4
\displaystyle \frac{4}{x-3}+\frac{3x+4}{6}=\frac{x}{2}
From Formulas: Primes and Subscripts, exercise 3
Solve each formula for the letter named. Type subscripts as plain digits or with an underscore: W_1 is W1 or W_1; type \pi as pi, as in K/(2pi H).
5
Solve for R: C = 2\pi R.
From Problems: Work and Motion, exercise 31
Give fractional answers as fractions or mixed numbers, like 12/13 or 4 5/12.
6
A can do a piece of work in 3\frac12 days, B in 2\frac45 days, and A, B, and C together can do it in 1\frac16 days. In how many days can C do the work alone?
From Equations with Decimals, exercise 2
Solve. Decimal answers like 1.42 are fine.
7
\displaystyle .15x-.4x=235x-2352.5
From Problems: Numbers, Ages, Money, and Areas, exercise 26
Write an equation, solve it, and check the answer against the words of the problem.
8
A man bought apples at 18 cents per dozen. He sold \frac15 of them at the rate of 3 for 4 cents, and the remainder at the rate of 4 for 3 cents, losing 76 cents. How many did he buy?
From Clearing an Equation of Fractions, exercise 23
Solve each equation and check. Type the root, like x = 3, -5/2, or 2c. If every number is a root, type any; if none is, type none.
9
\displaystyle \left(x-\frac{3}{2}\right)\left(x+\frac{2}{3}\right)-\left(x-\frac{1}{3}\right)^2-1\tfrac{1}{9}=0
From Problems: Work and Motion, exercise 27
Give fractional answers as fractions or mixed numbers, like 12/13 or 4 5/12.
10
A can do a piece of work in 2 days, B in 3 days, and C in 4 days. How long will it take them, working together?