Question

Translate each of the following verbal statements into equations and solve. Let \(x\) represent the unknown number. a. The quotient of a number and 5.3 is \(-6.7\) b. A number times 3.6 is 23.4 c. 42.75 is the product of a number and \(-7.5\) d. A number divided by 2.3 is 13.2 e. \(-9.4\) times a number is 47

Short answer

Answer: The values of x for the given verbal statements are: a. x = -35.51 b. x = 6.5 c. x = -5.7 d. x = 30.36 e. x = -5

Step-by-step solution

Translate verbal statement into an equation

The quotient of a number and 5.3 can be represented as \(\frac{x}{5.3}\). We are given that this quotient is equal to \(-6.7\). So, the equation is: $$ \frac{x}{5.3} = -6.7 $$

Solve the equation

In order to solve this equation, multiply both sides by 5.3: $$ x = 5.3 \times -6.7 $$ Now, calculate the value of x: $$ x = -35.51 $$ b. A number times 3.6 is 23.4

Translate verbal statement into an equation

A number times 3.6 can be represented as \(3.6x\). We are given that this product is equal to 23.4. So, the equation is: $$ 3.6x = 23.4 $$

Solve the equation

In order to solve this equation, divide both sides by 3.6: $$ x = \frac{23.4}{3.6} $$ Now, calculate the value of x: $$ x = 6.5 $$ c. 42.75 is the product of a number and \(-7.5\)

Translate verbal statement into an equation

The product of a number and \(-7.5\) can be represented as \(-7.5x\). We are given that this product is equal to 42.75. So, the equation is: $$ -7.5x = 42.75 $$

Solve the equation

In order to solve this equation, divide both sides by \(-7.5\): $$ x = \frac{42.75}{-7.5} $$ Now, calculate the value of x: $$ x = -5.7 $$ d. A number divided by 2.3 is 13.2

Translate verbal statement into an equation

A number divided by 2.3 can be represented as \(\frac{x}{2.3}\). We are given that this quotient is equal to 13.2. So, the equation is: $$ \frac{x}{2.3} = 13.2 $$

Solve the equation

In order to solve this equation, multiply both sides by 2.3: $$ x = 2.3 \times 13.2 $$ Now, calculate the value of x: $$ x = 30.36 $$ e. \(-9.4\) times a number is 47

Translate verbal statement into an equation

\(-9.4\) times a number can be represented as \(-9.4x\). We are given that this product is equal to 47. So, the equation is: $$ -9.4x = 47 $$

Solve the equation

In order to solve this equation, divide both sides by \(-9.4\): $$ x = \frac{47}{-9.4} $$ Now, calculate the value of x: $$ x = -5 $$