Chapter 1.8, Problem 42PPE

To determine

To Explain: How can a verbal sentence can be translated into an algebraic equation:

Answer to Problem 42PPE

Explanation of Solution

Calculation:

In order to translate a verbal sentence into an algebraic equation, we have to look for the key words and their respective expression as shown in the table below:

Operation	Key word	Example	Translation
Addition(+)	the sum of	The sum of x and 5	$x+5$
	more than	5 more than y	$y+5$
	plus	3 plus 4	$3+4$
	increased by	7 is increased by 2	$7+2$
Substraction	Minus	20 minus 10	$20-10$
	Less than	5 less than a number	$x-5$
	difference of	The difference of 100 and 90	$100-90$
	decreased by	A number is decreased by 5	$x-10$
Multiplication	Times	7 times x	$7\cdot x$
	Product of	the product of 7 and 8	$7\cdot 8$
	multiplied by	A number is multiplied by 4	$4\cdot x$
	of	three-fourth of a number	$\frac{3}{4}\cdot x$
Division	Divided by	10 divided by 5	$\frac{10}{5}$
	the quotient of	The quotient of 12 and 4	$\frac{12}{4}$
	the ratio of	The ratio of a number to 50	$\frac{x}{50}$
Power	squared of, squared	the square of a number, a number squared	$x^2$
	cube of, cubed	the cube of a number, a number cubed	$x^3$
Equals	is	2 times a number is 4	$2\cdot x=4$
	Is the same as	9 is same as thrice a number	$3\cdot x=9$
	yeilds	2 added to a number yeilds 5	$2+x=5$
	amounts to	10 less than a number amounts to 20	$x-10=20$