Maths Olympiad Prep

Library / /205 of 520

Algebra Difficulty 3.1 AMC 10/12 Find the answer

At the start of operation, the temperature inside a refrigerator is 12∘C12^{\circ}\mathrm{C}. If the temperature inside the refrigerator decreases by 5∘C5^{\circ}\mathrm{C} per hour, then after 44 hours, the temperature inside the refrigerator is ______.

A number or a short expression. Spacing and $ signs are ignored.

Solution

To find the temperature inside the refrigerator after 44 hours, we start with the initial temperature and then account for the decrease in temperature over time. The temperature decreases by 5∘C5^{\circ}\mathrm{C} each hour. Thus, after 44 hours, the total decrease in temperature is 5∘C×45^{\circ}\mathrm{C} \times 4 hours.

Starting with the initial temperature, we have:
Final Temperature=Initial Temperature+(Change in Temperature per Hour×Number of Hours)=12∘C+(−5∘C×4)=12∘C+(−20∘C)=−8∘C.\begin{align*} \text{Final Temperature} &= \text{Initial Temperature} + (\text{Change in Temperature per Hour} \times \text{Number of Hours}) \\ &= 12^{\circ}\mathrm{C} + (-5^{\circ}\mathrm{C} \times 4) \\ &= 12^{\circ}\mathrm{C} + (-20^{\circ}\mathrm{C}) \\ &= -8^{\circ}\mathrm{C}. \end{align*}

Therefore, the temperature inside the refrigerator after 44 hours is −8∘C\boxed{-8^{\circ}\mathrm{C}}.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.