Answer:
System of inequalities:
[tex]3x+2y \leq 25[/tex] , [tex] 4x+6y \leq 37[/tex]
1) Maximum number of sundaes possible = 9
2) Maximum number of milkshakes possible = 6
3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoop of ice-cream and 1 scoop of strawberries.
Step-by-step explanation:
Given : A sundae requires 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.
Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x denote the number of sundaes he makes and y the number of milkshakes he makes.
First we represent in tabular form,
Sundae(x) Milkshake(y) Total
Ice-cream 3 2 3x+2y
Strawberries 4 6 4x+6y
→System of inequalities:
Sundaes and milkshake with at most 25 ice-cream scoops= [tex]3x+2y \leq 25[/tex]
Sundaes and milkshakes with at most 37 strawberries = [tex] 4x+6y \leq 37[/tex]
→ Plotting the equations in the graph (figure attached)
1) Maximum number of sundaes possible:
Maximum no. of sundaes possible when y=0
From the graph y=0 at x=9.25
Therefore, Maximum number of sundaes possible is 9
2) Maximum number of milkshakes possible:
Maximum no. of milkshakes possible when x=0
From the graph x=0 at y= 6.167
Therefore, Maximum number of milkshakes possible is 6
3) Combination that uses the most of both Ice-cream and Strawberries:
Combination of both is possible there is a intersection of both the equation
From the graph intersection point is x=7.6 and y=1.1
Therefore, Combination that uses the most of both Ice-cream and Strawberries = 7 scoop of ice-cream and 1 scoop of strawberries.
Answer: for the people who's question is a little different and on Khan Academy...
inequality that represents the condition based on the number of ice cream scoops: 3S+2M≤25
inequality that represents the condition based on the number of strawberries:
4S+6M≤37
Step-by-step explanation:
We are given that a sundae requires 3 ice-cream scoops, and a milkshake requires 2 ice-cream scoops.
How can we express the total number of ice-cream scoops Ramses expects to use?
The number of ice-cream scoops required to make S sundaes is 3S, S, and the number of ice-cream scoops required to make M milkshakes is 2M. Therefore, the total number of ice-cream scoops Ramses expects to use is 3S+2M.
We are also given that Ramses has at most 25 ice-cream scoops. Let's use this to create the appropriate inequality:
3S+2M≤25
Similarly, the number of strawberries required to make S sundaes is 4S, and the number of strawberries required to make M milkshakes is 6M. Since we are also given that Ramses has at most 37 strawberries, this is the appropriate inequality:
4S+6M≤37
proof lol:
