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, the bathroom has enough water and shampoo for all of them.

Step-by-step explanation:

70L+ 60S < 5600

Putting 8 into L and 7 into S, gives:

70(8) + 60(7) = 560 + 420 = 980

That is definitely less than 5600, so water is OK.

Now,

0.02L + 0.01S

Putting 8 into L and 7 into S, gives:

0.02(8) + 0.01(7) = 0.16 + 0.07 = 0.23

That's definitely less than 2.5 liters, so shampoo is OK as well.

Hence, bathroom has enough water and shampoo for them.

Step-by-step explanation:

This problem can solved just by replacing the given values into the give inequalities. The first inequality:

Refers to the maximum amount of water.

The second inequality:

Refers to the maximum amount of shampoo.

Then, the problem as is there's enough water en shampoo for 8 long-haired and 7 short-haired members, where L is long-haired and S is short-haired. Now, replacing this values in each inequality, we have:

Definitely, there's way enough water to 8 long-haired and 7 short-haired, because the maximum is 5600, and they only spend 980.

We see that there's enough shampoo too, because the maximum is 2.5, and these people only use 0.23.

Therefore, the bathroom have enough water and shampoo for 8 long-haired members and 7 short-haired members.