+47 Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter.
The food and medication for each dog costs twice as much as those supplies for a cat
. She needs to feed 164 cats and 24 dogs. Her budget is $4240.
Write a system of equations that models the above situation (be sure to define what each variable represents) How much can Margie spend on each dog for food and medication
+129850 Call the amount spent on each, cat, x and let the amount spent each dog = y = 2x
So we have the following constraints
y = 2x (1)
164(x) + 24y <= 4240 (2)
Substituting (1) into 2 for y, we have
164x + 24(2x) <= 4240 simplify
212x <= 4240 divide both sides by 212
x<= $20 on each cat
And y = 2(20) = $40 on each dog
So.....it appears that she can spend $20 on each cat and $40 on each dog
This is confirmed by the following graph : https://www.desmos.com/calculator/vcobwbtcdd
The optimum expenditure occurs at the corner point of the intersection of the line y= 2x and the graph of (2) above.....i.e., at the point (20,40)
+129850 Call the amount spent on each, cat, x and let the amount spent each dog = y = 2x
So we have the following constraints
y = 2x (1)
164(x) + 24y <= 4240 (2)
Substituting (1) into 2 for y, we have
164x + 24(2x) <= 4240 simplify
212x <= 4240 divide both sides by 212
x<= $20 on each cat
And y = 2(20) = $40 on each dog
So.....it appears that she can spend $20 on each cat and $40 on each dog
This is confirmed by the following graph : https://www.desmos.com/calculator/vcobwbtcdd
The optimum expenditure occurs at the corner point of the intersection of the line y= 2x and the graph of (2) above.....i.e., at the point (20,40)
