Chapter 9.7, Problem 38CCR

a.

To determine

To represent:the given situation by an equation.

Answer to Problem 38CCR

The equation representing the situation is:

  $y=3+12x$

Explanation of Solution

Given:

Gabe’s age is $3$ years more than twelve times Briana’s age $x$ .

Calculation:

As per the given problem

Let Gabe’s age be $y$ .

Therefore, the equation representing the situation is:

  $y=3+12x$

b.

To determine

To find: four solutions to the equation (obtained in part (a)).

Answer to Problem 38CCR

The four solutions of $y=3+12x$ are $(1,15),(2,27),(3,39),\text{ and }(4,51)$ .

Explanation of Solution

Given:

The equation (obtained in part(a)) representing the situation is:

  $y=3+12x$

Concept used:

Step 1: Choose four values for $x$ and substitute each value into the equation.

Step 2: evaluate the expression to find the value of $y$ .

Step 3: write the solutions as ordered pairs.

Calculation :

As per problem,

Consider the given equation:

  $y=3+12x$

As $x$ represents Briana’s age it cannot be a negative value or $0$ .

Choose four positive integer values of $x$ , such as $1,2,3,4$ . Substitute these values in the equation and evaluate to find the value of $y$ . Then, write the solutions as ordered pairs.

The values of $y$ and solution pairs for respective values of $x$ are:

Therefore, the four solutions of $y=3+12x$ are $(1,15),(2,27),(3,39),\text{ and }(4,51)$ .