Question

Please help, worth 40 points!!!

1. The soccer team raised $31.50 by selling 42 bottles of water. Write an equation with a variable that can be solved to find the price of each bottle of water. Solve your equation. How do you know your answer is correct?

2. What would the graph of an equation look like on a number line? (Use an example)

Answer 1

To find the price of each bottle of water, we can set up an equation with a variable representing the price per bottle. Let's use "x" as the price per bottle in dollars:

Total money raised = Price per bottle × Number of bottles

$31.50 = x × 42

Now, we can solve for "x":

x = $31.50 / 42

x = $0.75

So, each bottle of water costs $0.75.

To check if the answer is correct, we can multiply the price per bottle by the number of bottles and see if it matches the total money raised:

$0.75 × 42 = $31.50

The result matches the total money raised, confirming that the answer is correct.

Regarding the second question about the graph of an equation on a number line, number lines typically represent single-variable linear equations. An example of a linear equation is:

y = 2x + 3

On a number line, we would plot the points that satisfy this equation. For example, if we choose some values for "x," we can find the corresponding "y" values using the equation. Let's say:

x = -2, then y = 2(-2) + 3 = -1

x = 0, then y = 2(0) + 3 = 3

x = 2, then y = 2(2) + 3 = 7

We can plot these points on the number line and connect them with a straight line, as it's a linear equation. The graph would look like:

-4 -3 -2 -1 0 1 2 3 4

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-1--|--|--|--|--|--|--|--|-

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| | | | | | | | |

3--|--|--|--|--|--|--|--|-

| | | | | | | | |

| | | | | | | | |

| | | | | | | | |

The graph represents the line y = 2x + 3 on the number line

Answer 2

1. The answer to the first question is that each bottle of water costs $0.75. You can find this by solving the equation: $0.75 × 42 = $31.50.

2. The answer to the second question is a point marked on the number line at the value of the solution. For the example equation "x + 2 = 5," the solution is x = 3. So, the number line would have a point marked at the position 3, as shown in the illustration in my previous response.

Explanation:

1. Let's denote the price of each bottle of water as "p" (in dollars). The given information can be represented in an equation:

Total amount raised = Price per bottle × Number of bottles sold

$31.50 = p × 42

To solve for "p," divide both sides of the equation by 42:

p = $31.50 / 42

p = $0.75

So, each bottle of water costs $0.75. To verify that this answer is correct, you can substitute the value of "p" back into the equation and see if it satisfies the given information:

$0.75 × 42 = $31.50

Since the left-hand side of the equation equals the right-hand side, the solution is correct.

2. An equation graph on a number line represents the solution set of that equation. Let's take the equation "x + 2 = 5" as an example.

To represent this on a number line:

- Mark a point at the number 5, as this is the value we are trying to achieve (the right-hand side of the equation).

- Since the equation is "x + 2 = 5," the variable "x" is two less than 5. So, mark another point two units to the left of 5.

Now, connect the two points with a line. This line represents the solution to the equation. In this case, the point where the line intersects the number line is the solution for "x," which is 3.

This point represents the value of "x" that satisfies the equation "x + 2 = 5."

In general, on a number line, an equation graph would be a point or points that correspond to the solution(s) of the equation, marked appropriately based on the equation's variables and constants.