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. 70 L+60 S < 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. 0.02 L+0.01 S <= 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?

Check Water Inequality: Check if there is enough water for 8 long-haired members and 7 short-haired members using the water inequality. 70L + 60S < 5600 Substitute L with 8 and S with 7. 70(8) + 60(7) < 5600 560 + 420 < 5600 980 < 5600Check Shampoo Inequality: Check if there is enough shampoo for 8 long-haired members and 7 short-haired members using the shampoo inequality. 0.02L + 0.01S <= 2.5 Substitute L with 8 and S with 7. 0.02(8) + 0.01(7) <= 2.5 0.16 + 0.07 <= 2.5 0.23 <= 2.5Verify Conditions: Determine if both conditions are satisfied for water and shampoo. From Step 1, we have 980 < 5600, which means there is enough water. From Step 2, we have 0.23 <= 2.5, which means there is enough shampoo. Both conditions are satisfied.

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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. $\newline$ 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. $\newline$ $0.02L + 0.01S \leq 2.5$ represents the number of long-haired members and short-haired members who can wash their hair with at most $2.5$ liters of shampoo. $\newline$ Does the bathroom have enough water and shampoo for $8$ long-haired members and $7$ short-haired members?

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Q. 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.

\newline

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.

\newline

0.02L + 0.01S \leq 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.

\newline

Does the bathroom have enough water and shampoo for

8

long-haired members and

7

short-haired members?

Check Water Inequality: Check if there is enough water for $8$ long-haired members and $7$ short-haired members using the water inequality. $\newline$ 70L + 60S < 5600 $\newline$ Substitute $L$ with $8$ and $S$ with $7$ . $\newline$ 70(8) + 60(7) < 5600 $\newline$ 560 + 420 < 5600 $\newline$ 980 < 5600
Check Shampoo Inequality: Check if there is enough shampoo for $8$ long-haired members and $7$ short-haired members using the shampoo inequality. $\newline$ $0.02L + 0.01S \leq 2.5$ $\newline$ Substitute $L$ with $8$ and $S$ with $7$ . $\newline$ $0.02(8) + 0.01(7) \leq 2.5$ $\newline$ $0.16 + 0.07 \leq 2.5$ $\newline$ $0.23 \leq 2.5$
Verify Conditions: Determine if both conditions are satisfied for water and shampoo. $\newline$ From Step $1$ , we have 980 < 5600, which means there is enough water. $\newline$ From Step $2$ , we have $0.23 \leq 2.5$ , which means there is enough shampoo. $\newline$ Both conditions are satisfied.