Answer:
System of inequalities:
, 
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=
Sundaes and milkshakes with at most 37 strawberries =
→ 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.
