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以下是一则新闻消息：“今天零时，发改委将汽油、柴油价格每吨分别降低125元和120元，测算到零售价格92号汽油和0号柴油每升分别降低0.09元和0.10元……”...

Mar 19, 2024

以下是一则新闻消息：“今天零时，发改委将汽油、柴油价格每吨分别降低125元和120元，测算到零售价格92号汽油和0号柴油每升分别降低0.09元和0.10元……”，据此估测92号汽油的密度为______kg/m。小聪爸爸给小汽车加油50L，一共加注______kg的92号汽油。

Solution

Calculate the decrease in price per liter for 92号汽油 (92 octane gasoline). Given that the price decreases by 0.09元 per liter

Calculate the total decrease in price for one ton of 92号汽油. Since 1 ton = 1000 kg, the total decrease is 125元 per ton

Estimate the density of 92号汽油. Density is mass per unit volume. Use the formula

\rho = \frac{m}{V}

where

\rho

is the density,

m

is the mass, and

V

is the volume. We have the decrease in price per liter (from step a) and the total decrease in price for one ton (from step b), so we can set up the equation

0.09元/L = \frac{125元}{\rho \cdot 1000L}

and solve for

\rho

Solve for the density

\rho

of 92号汽油. Rearrange the equation from step c to get

\rho = \frac{125元}{0.09元/L \cdot 1000L}

and calculate the density

Calculate the mass of 92号汽油 that 小聪爸爸 adds to the car. Use the formula

m = \rho \cdot V

, where

V = 50L

is the volume of gasoline added

Answer

Density of 92号汽油:

\rho = \frac{125}{0.09 \cdot 1000}

kg/L

Mass of 92号汽油 added to the car:

m = \rho \cdot 50L

Key Concept

Density and its calculation: Density is a measure of mass per unit volume. The formula to calculate density is

\rho = \frac{m}{V}

Explanation

By knowing the decrease in price per liter and per ton, we can estimate the density of the gasoline. Then, using the density and the volume of gasoline added to the car, we can calculate the total mass of gasoline.