Question

omar will donate up to $500 to charity. the money will be divided between two charities: the city of youth fund and educational growth foundation. omar 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 the requirements.

Answer 1

Please refer to the attached graph

Explanation:

Knowing the following:

X = amount of money donated to the city youth fund

Y = amount of money donated to the educational growth foundation

We can write the statements in form of equations:

"Will donate up to $500, the money will be divided between two charities"

(a)
`X + Y = \$ 500`

"The amount donated to the educational growth foundation to be at least four times the amount donated to the city youth fund"

(b)
`Y \geq 4X`

If we graph both equations we can see the area where both conditions are met (see graph attached)

Where the blue line is (a) and the red line is (b)

Shaded area represent all the possible solutions for the donations, for example:

X=100 and Y=400 or

X=50 and Y=200, etc.