Question

A sundae requires 33 ice-cream scoops and 44 strawberries, and a milkshake requires 22 ice-cream scoops and 66 strawberries. Ramses wants to make sundaes and milkshakes with at most 2525 ice-cream scoops and 3737 strawberries. Let SS denote the number of sundaes he makes and MM 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.

Answer 1

3S+2M≤25

4S+6M≤37

Answer 2

Inequality based on number of ice-cream scoops:
`3S+2M\leq 25`

Inequality based on number of strawberries:
`4S+6M\leq 37`.

Explanation:

Let S be the number of sundaes and M be number of milkshakes Ramses makes.

We have been given that a sundae requires 3 ice-cream scoops and 4 strawberries. A milkshake requires 2 ice-cream scoops and 6 strawberries.

The number of ice-cream scoops used in making S Sundaes will be 3S. The number of ice-cream scoops used in making M milkshakes will be 2M.

As Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops, so the inequality representing the condition based on the number of ice-cream scoops will be:

`3S+2M\leq 25`

The number of strawberries used in making S Sundaes will be 4S. The number of strawberries used in making M milkshakes will be 6M.

As Ramses wants to make sundaes and milkshakes with at most 37 strawberries, so the inequality representing he condition based on the number of strawberries will be:

`4S+6M\leq 37`