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?

Answer 1

The bathroom have enough water and shampoo.

Explanation:

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

`70L+ 60S < 5600`

Refers to the maximum amount of water.

The second inequality:

`0.02L + 0.01S\leq 2.5`

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:

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

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

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

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.

Answer 2

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

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.