Question

1.2 writing equations worksheet
translate each sentence into an equation or formula.

1. two added to three times a number m is the same as 18.

1. twice a increased by the cube of a equals b.

1. seven less than the sum of p and q is as much as six.

1. the sum of x and its square is equal to y times z.

1. four times the sum of f and g is identical to six times g.

1. the perimeter p of a square equals four times the length of a side s.

1. the area a of a square is the length of a side s squared.

1. the perimeter p of a triangle is equal to the sum of the lengths of sides a, b, and c.

1. the area a of a circle is π times the radius r squared.

Explanation:

1)

Step1: Analyze the sentence

"Two added to three times a number \( m \) is the same as 18."
"Three times a number \( m \)" is \( 3m \), "two added to" that is \( 3m + 2 \), and this equals 18.

Step2: Write the equation

\( 3m + 2 = 18 \)

Step1: Analyze the sentence

"Twice \( a \) increased by the cube of \( a \) equals \( b \)."
"Twice \( a \)" is \( 2a \), "the cube of \( a \)" is \( a^3 \), "increased by" means add, so combine them and set equal to \( b \).

Step2: Write the equation

\( 2a + a^3 = b \)

Step1: Analyze the sentence

"Seven less than the sum of \( p \) and \( q \) is as much as six."
"The sum of \( p \) and \( q \)" is \( p + q \), "seven less than" that is \( (p + q)- 7 \), and this equals 6.

Step2: Write the equation

\( (p + q)- 7 = 6 \)

Answer:

\( 3m + 2 = 18 \)

2)