Question

Members of the swim team want to wash their hair. The bathroom has less than 560056005600 liters of water and at most 2.52.52, point, 5 liters of shampoo. 70L+60S < 560070L+60S<560070, L, plus, 60, S, is less than, 5600 represents the number of long-haired members LLL and short-haired members SSS who can wash their hair with less than 560056005600 liters of water. 0.02L+0.01S \leq 2.50.02L+0.01S≤2.50, point, 02, L, plus, 0, point, 01, S, is less than or equal to, 2, point, 5 represents the number of long-haired members and short-haired members who can wash their hair with at most 2.52.52, point, 5 liters of shampoo. Does the bathroom have enough water and shampoo for 888 long-haired members and 777 short-haired members?

Answer 1

Answer:

Yes, both shampoo and water will be enough

Given that:

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

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

L = long-haired ; S = short-haired

70L+ 60S < 5600

Check the constraint for amount of water :

70L+ 60S < 5600

L = 8 ; S = 7

70(8) + 60(7) < 5600

560 + 420 < 5600

980 < 5600

Constraint satisfied

Number of long and short hair member who can wash their hair with shampoo not more than 2.5 litres

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 (constraint satisfied).