Dan will donate up to $480 to charity. The money will be divided between two charities: the City Youth Fund and the Educational Growth Foundation. Dan would like to donate at least
to the Educational Growth Foundation. He would also like the amount donated to the Educational Growth Foundation to be at least four times the amount donated to the City Youth Fund. Let x denote the amount of money (in dollars) donated to the City Youth Fund. Let y denote the amount of money (in dollars) donated to the Educational Growth Foundation. Shade the region corresponding to all values of x and y that satisfy these requirements.
Hi Jacob;
Have you considered the two equation (then their inequalities) that have to be considered.
You know
1) x + y = 480 the money divided up
2) y = 4x as he would like to donate four times the amount to the youth fund.
If you graph these two lines then check the inequalities you can work out the shaded regions.
How do you work the Formula
Well, we have some conditions to satisfy here. First, let's define our variables:
x = amount donated to City Youth Fund (in dollars)
y = amount donated to Educational Growth Foundation (in dollars)
Now, let's break down the given conditions:
1. Dan will donate up to $480.
This means that the total amount donated should be less than or equal to $480, so we have the inequality:
x + y ≤ 480
2. Dan wants to donate at least [insert value] to the Educational Growth Foundation.
We're missing the value here, but let's call it z. So,
y ≥ z
3. The amount donated to the Educational Growth Foundation should be at least four times the amount donated to the City Youth Fund.
This can be expressed as:
y ≥ 4x
Combining all these conditions, we have the following system of inequalities:
x + y ≤ 480
y ≥ z
y ≥ 4x
Now, if you want me to shade the region corresponding to all values of x and y that satisfy these requirements, I'm afraid I can't do that. You see, I'm a bot, and I'm not equipped with visual capabilities. But I can tell you that the region you're looking for is the area where all three conditions overlap. You can plot these inequalities on a graph and shade the overlapping region manually.
To find the region corresponding to all values of x and y that satisfy the given requirements, we need to set up some equations based on the given information.
Let x be the amount of money donated to the City Youth Fund.
Since the total amount donated should be $480, we can find the amount donated to the Educational Growth Foundation by subtracting x from the total amount:
y = $480 - x
We want the amount donated to the Educational Growth Foundation to be at least four times the amount donated to the City Youth Fund:
y ≥ 4x
Also, Dan wants to donate at least $___ to the Educational Growth Foundation. Unfortunately, you did not provide a specific amount that should be donated. Please provide the missing information so that I can help you shade the region corresponding to the requirements.