Question

A grocery bag contains x apples, each weighing of a pound, and y pounds of grapes. The total weight of the grocery bag is less than 5 pounds. Which graph represents the possible numbers of apples and pounds of grapes that can be in the bag?

Answer 1

First let's write out the inequality before choosing a graph.

x apples each weighing 1/3 of a pound: 1/3x

y pounds of grapes: y

So...

1/3x + y < 5

The maximum weight is 4 pounds since the total weight of both the grapes and apples are less than 5.

In the y-axis, the first, third, and fourth graphs already exceed the capacity of 5 pounds.

So, by process of elimination, the correct graph for this problem is the second one.

Answer 2

The correct graph option is $\boxed{\bf option 2}$.

Further explanation:

Given:

The number of apples in the bag is $x$.

The weight of each apple is $\frac{1}{3}\text{ pound}$.

The total weight of the grocery bag is less than $5\text{ pounds}$.

Calculation:

The weight of $x$ apple is $\frac{x}{3}\text{ pounds}$.

The weight of the grapes is $y$ pound.

Write the inequality of the above equation.

$\boxed{\dfrac{1}{3}x+y$       …… (1)

Substitute $0$ for $y$ in equation (1) to obtain the value of $x$ as follows:

$\begin{aligned}\dfrac{x}{3}+y&$

Substitute $0$ for $x$ in equation (1) to obtain the value of $y$ as follows:

$\begin{aligned}\dfrac{1}{3}\left(0\right)+y&$

Now check the option to find the correct graph for the above inequality.

First graph shows the value of $x$ is greater than $15$ which is not correct.

Second graph shows the value of $x$ is less than $15$ and value of $y$ is less than $5$.

Third graph shows the value of $x$ is greater than $5$ which is not correct.

Fourth graph shows the value of $x$ is less than $15$ which is not correct.

Therefore, the correct option is $\boxed{\bf option 2}$.

Learn more:

1. Representation of graph brainly.com/question/2491745

2. Equation of line brainly.com/question/1473992

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Linear inequality

Keywords:  Graph, inequality, apple, grapes, pound, weight, grocery, grocery bag, 5 pounds, x apples, y pounds grapes, total weight.