Asundae 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's form a system of inequalities to represent his conditions. let x denote the number of sundaes he makes and y the number of milkshakes he makes. maximum number of sundaes possible: maximum number of milkshakes possible: combination that uses the most of both ice-cream and strawberries:

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.