Question 1191485: Translate to a system of inequalities and solve.
Jocelyn is pregnant and needs to eat at least 400 more calories a day than usual. When buying groceries one day with a budget of $15 for the extra food, she buys bananas that have 90 calories each and chocolate granola bars that have 150 calories each. The bananas cost $0.35 each and the granola bars cost $2.50 each.
(a)
Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)
(b)
Graph the system.
(c)
Could she buy 6 bananas and 6 granola bars?
(d)
Could she buy 3 bananas and 3 granola bars?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's your graph.
using the desmos.com graph, you graph the opposite of the inequalities.
the area of the graph that is not shaded is your region of feasibility.
that and the points on the line if the inequalities are <= or >=, rather than < or >.
you can see from the graph that the point (0,6) is one of the corner points of the feasible region.
answers to your questions are below:
(a)
Write a system of inequalities to model this situation. (Let b represent the bananas bought and let g represent the number of granola bars bought. Enter your answers as a comma-separated list of inequalities.)
the inequalities are:
.35x + 2.5y <= 15
90x + 150y >= 400
first equation models the cost.
second equation models the calories.
(b)
Graph the system.
done.
(c)
Could she buy 6 bananas and 6 granola bars?
no, she cannot buy 6 bananas and 6 granola bars.
you can see from the graph that the point (6,6) is not in the region of feasibility.
an evaluation of the equations at (6,6) shows you why.
.35x + 2.5y = 17.1 which is not less than or equal to 15.
90x + 150y = 1440 which is greater than 400.
first constraint is not satisfied.
second constraint is.
both must be satisfied, otherwise the point is not valid.
(d)
Could she buy 3 bananas and 3 granola bars?
yes, she can buy 3 banancas and 3 granola bars.
you can see from the graph that the point (3,3) is in the region of feasibility.
an evaluation of the inequalities will show that they are both true.
.35x + 2.5y = 8.55 which is less than 15.
90x + 1.5y = 720 which is greater than 400.
both constraints are satisfied as they need to be for the point to be feasible.
let me know if you have any questions or concerns.
theo
|
|
|
