Does the bathroom have enough water and shampoo for 888 long-haired members and 777 short-haired members?

Complete question :

Members of the swim team want to wash their hair. The bathroom has less than 5600 liters of water and at most 2.5 liters of shampoo. 70L+ 60S < 5600 represents the number of long-haired members L and short-haired members S who can wash their hair with less than 5600 liters of water. 0.02L + 0.01S < or equal to 2.5 represents the number of long-haired members and short-haired members who can wash their hair with at most 2.5 liters of shampoo. Does the bathroom have enough water and shampoo for 8 long-haired members and 7 short -haired members?

Yes , there is enough water and shampoo

Step-by-step explanation:

Given that:

Number of long and short hair member who can wash their hair with less than 5600 litres of water.

70L+ 60S < 5600

Number of long and short hair member who can wash their hair with at most 2.5 litres of shampoo

0.02L + 0.01S ≤ 2.5

To check if bathroom has enough water and shampoo for 8 long haired and 7 short haired members.

Water check:

70L+ 60S < 5600

L = 8 ; S = 7

70(8) + 60(7) < 5600

560 + 420 < 5600

980 < 5600

Inequality constraint is satisfied ; There is enough water.

Shampoo check:

0.02L + 0.01S ≤ 2.5

L = 8 ; S = 7

0.02(8) + 0.01(7) ≤ 2.5

0.16 + 0.07 ≤ 2.5

0.23 ≤ 2.5

Inequality constraint is satisfied ; There is enough shampoo

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