The cheerleaders at the high school need to earn money to help pay for their uniforms. They plan to have a fundraiser selling two different types of chocolate bars.
They need to earn at least $200.
For every chocolate bar with a peanut butter filling (y) that they sell, they will make a profit of $0.80.
For every chocolate bar with almonds (x) that they sell, they will make a profit of $1.00.
Write an inequality to model this situation and graph the inequality on the grid at the left to show all the possible solutions. Be sure to label your graph.
Let x be the number of chocolate bars with almonds sold.
Let y be the number of chocolate bars with peanut butter filling sold.
The total profit from selling chocolate bars with almonds is $1.00x.
The total profit from selling chocolate bars with peanut butter filling is $0.80y.
To earn at least $200, the total profit should be greater than or equal to $200.
Therefore, the inequality to model this situation is:
$1.00x + $0.80y ≥ $200.
To graph this inequality, we first plot the line $1.00x + $0.80y = $200.
To do this, we can solve the equation for y:
$0.80y = $200 - $1.00x
y = ($200 - $1.00x)/$0.80
Next, we find two points that lie on this line. We can choose x-intercept and y-intercept values for convenience.
When x = 0, y = ($200 - $1.00(0))/$0.80 = $200/$0.80 = 250.
So (0, 250) is a point on the line.
When y = 0, x = ($200 - $1.00y)/$1.00 = $200/$1.00 = 200.
So (200, 0) is a point on the line.
Plotting these points and drawing the line that connects them, we get:
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The shaded region above the line represents all the possible solutions.