The temperature is $60^{\circ} F$. The temperature will decrease by $3^{\circ} F$ each hour. Let $h$ be the number of hours.
When will the temperature be below $32^{\circ} F$?
Write an inequality for this problem.
A. $60+3 h<32$
B. $60+3 h \leq 32$
C. $60-3 h \leq 32$
D. $60-3 h<32
Answer (1)
The initial temperature is 6 0 ∘ F , and it decreases by 3 ∘ F each hour.
Express the temperature after h hours as 60 − 3 h .
Set up the inequality 60 − 3 h < 32 to represent when the temperature is below 3 2 ∘ F .
The correct inequality is 60 − 3 h < 32 .
Explanation
Understanding the Problem The problem states that the initial temperature is 6 0 ∘ F and it decreases by 3 ∘ F each hour. We need to find an inequality that represents when the temperature will be below 3 2 ∘ F .
Expressing the Temperature Let h be the number of hours. The temperature after h hours can be expressed as 60 − 3 h . We want to find when this temperature is less than 3 2 ∘ F .
Formulating the Inequality We can write the inequality as: 60 − 3 h < 32
Identifying the Correct Option Now, we compare this inequality with the given options: A. 60 + 3 h < 32 B. 60 + 3 h ≤ 32 C. 60 − 3 h ≤ 32 D. 60 − 3 h < 32
The correct inequality is 60 − 3 h < 32 , which matches option D.
Examples
Imagine you're baking a cake, and the oven starts at 6 0 ∘ F . If the temperature drops by 3 ∘ F every minute after you turn it off, this problem helps you determine how long it will take for the oven to cool down to a safe temperature (below 3 2 ∘ F ) so you can safely handle the cake. Understanding inequalities helps in predicting and managing temperature changes in various real-life scenarios, from cooking to environmental monitoring.
