Sarah is buying roses and carnations to make center pieces for prom, Roses, x, cos $3 each and carnations, y, cost $1 each. She can spend no more than $75 on the
Flowers. Which graph represents the solution to the problem?

The correct graph is option 3.

Given,

Sarah buys x no. of roses and y no. of carnations.

The cost of each roses be $3, so cost of x roses be 3 x .

And the cost of each carnations be $1, so cost of y carnations be y.

The total cost will be  

But as given in question she can spend no more than $75, so we have the inequality  .

Writing the above equation as a line we have  .

So graph of above line will be a solid line with a negative slope and the shaded part will be below that line so the value of y goes in between 0 and 75.

Now, value of x when y is o will be calculated from  .

Now we have values of x in between 0 and 25.

here we have y in between 0 and 75 with a negative slope and x in between 0 and 25. so the shaded part will be below that line goes in between 0 and 75 on y axis . option 3 has shaded part in between 0 and 75 on y axis  so the correct option is 3.

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Third option.

Step-by-step explanation:

We have the variables:

x =  number of roses that Sarah buys

y = number of carnations that Sarah buys.

Each rose costs $3, then the price for x roses is: x*$3.

Each carnation costs $1, then the price for y carnations is: y*$1.

The total price will be:

$3*x + $1*y

And she can spend no more than $75, then we have the inequality:

$3*x + $1*y ≤ $75

Writing this as a line, we have:

y ≤ 75 - 3*x

Then the graph of this will be:

A solid line with a negative slope and the shaded part will be below that line.

The value of y goes between 0 and 75.

The value x goes between 0 and the value of x such y = 0, this is:

y = 0 ≤ 75 - 3*x

 3*x ≤ 75

     x ≤ 75/3 = 25

Then the value of x goes between 0 and 25.

The correct option will be the third one.

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