Question

Shen will donate up to $440 to charity. The money will be divided between two charities: the City Youth Fund and the Educational Growth Foundation. Shen would 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.

Answer 1

Answer:

Step-by-step explanation:

Let the amount donated to City Youth Fund = $x

And the amount donated to the Educational Growth Foundation = $y

Amount donated to the Educational Growth Foundation is at least four times the amount donated to City Youth Fund.

y ≥ 4x ------(1)

Total amount she can donate is up to $440

x + y ≤ 440 ------(2)

And the constraints are x ≥ 0 --------(3)

y ≥ 0 ------(4)

And solution set will be the common shaded area of both inequalities as shown in the graph attached.

(By using a graphing tool we can find the graph).

Answer 2

Following are the calculation to the given question:

$\to C+E=440\\\\\to E\geq 2C\\\\\to x+y = 440\\\\\to y \geq 2x\\\\\to y=440-x\\\\\to 440-x \geq 2x$

$\to -3x \geq -440$ multiply by$-\frac{1}{3}$ and switch the direction of the inequality sign

$\to x\leq \frac{440}{3} = \ 146.67$for the City Youth Fund

$\to y\leq \frac{2(440)}{3} = \ 253.33$ for the Educational Growth Fund

$\to 0 \leq x \leq \ 146.67\\\\\to \ 253.33 \leq y \leq \ 440$

OR

By using the given condition we find the equation that is:

$\to x+y \leq 440 \\\\\to y \geq 3x \\\\\to x, y \geq 0$

Please find the graph image in the attachment file.

• In this, the dark blue color portion defines the bounded by the region points that are $\bold{(0,0), (0,440), (110,330)}$.

Learn more:

brainly.com/question/2636727