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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 S denote the number of sundaes he makes and M the number of milkshakes he makes. Write an inequality that represents the condition based on the number of ice-cream scoops. Write an inequality that represents the condition based on the number of strawberries.​

Sagot :

The system of inequalities be

3x+2y ≤ 25, 4x+6y ≤ 37

1) Maximum number of sundaes possible exists 9.

2) Maximum number of milkshakes possible exists 6.

3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.

What is system of inequalities?

A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.

Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.

Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.

Let x represent the number of sundaes he creates and y the number of milkshakes he creates.

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 milkshakes with at most 25 ice-cream scoops exist

33x+2y ≤ 25.

Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.

1) Maximum number of sundaes possible:

Maximum number of sundaes possible when y = 0

From the graph y = 0 at x = 9.25

Therefore, the maximum number of sundaes possible exists at 9.

2) Maximum number of milkshakes possible:

Maximum number of milkshakes possible when x = 0

From the graph x = 0 at y = 6.167

Therefore, the maximum number of milkshakes possible exists at 6.

3) Combination that utilizes the most of both Ice-cream and Strawberries:

A combination of both is possible there exists an intersection of both the equation.

From the graph, the intersection point exists x = 7.6 and y = 1.1.

Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.

To learn more about system of inequalities refer to:

https://brainly.com/question/9290436

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