8. Mark wants to purchase a combination of at least 16 turkey subs or roast beef subs for a party. Each turkey sub, , is priced at $5 and each roast beef sub, , is priced at $4. Mark has at most $80 to spend on the subs.
A. Write a system of inequalities that can be used to model this situation.
B. Graph the inequalities on the axes provided.
C. Name one combination of subs that will allow Mark to stay within his budget.
Turkey subs ___________ Roast beef subs__________
D. Using the combination of hours you chose for part C, how much would Mark spend?
You told me the following
t + r ≥ 16
5t + 4r ≤ 80
take over
Can i solve by using the substitution method so multiply the t + r is greater than or equal to 16 equation by -4
am I on the right track?
You must be talking about C
since we are using ≥ and ≤ , we can use equations.
r = 16-t
sub into the 2nd
5t + 4(16-t) = 80
5t + 64 - 4t = 80
t = 16
then r = 0
I will leave it up to you to decide if "combination" would include the case of only one type of sub
The math certainly allows for that case.
If your ordered pairs are of the type (t,r)
my graph of your problem shows a triangle formed by the points
(16,0) , (0,6), and (0,20)
Any point in that region with integer values would work
Thanks I got it
How many turkey subs and how many roast beef subs
A. To model this situation, we can set up the following inequalities:
Let x represent the number of turkey subs and y represent the number of roast beef subs.
The cost of each turkey sub is $5, so the total cost of turkey subs can be represented as 5x.
The cost of each roast beef sub is $4, so the total cost of roast beef subs can be represented as 4y.
The first inequality represents that the combination of turkey subs and roast beef subs must be at least 16:
x + y ≥ 16
The second inequality represents that the total cost of subs must be at most $80:
5x + 4y ≤ 80
B. To graph these inequalities, we can plot the corresponding lines on a graph.
For the first inequality, x + y ≥ 16, we can plot the line x + y = 16 by setting x = 0 and solving for y, and setting y = 0 and solving for x. This will give us two points on the line, and we can connect them with a straight line.
For the second inequality, 5x + 4y ≤ 80, we can plot the line 5x + 4y = 80 by following the same process.
C. To find a combination that allows Mark to stay within his budget, we need to find a point that satisfies both inequalities. One possible combination is 8 turkey subs (x = 8) and 8 roast beef subs (y = 8).
D. Using the combination of 8 turkey subs and 8 roast beef subs, we can calculate the total cost:
Total cost = (Cost of turkey subs * Number of turkey subs) + (Cost of roast beef subs * Number of roast beef subs)
Total cost = (5 * 8) + (4 * 8)
Total cost = 40 + 32
Total cost = $72
Therefore, Mark would spend $72 on this combination.