Question

If \[\dfrac{3}{4}\] of a gallon of paint covers \[\dfrac{2}{5}\] of a wall, then how many gallons are needed to paint the entire wall?

Answer 1

Hint: To solve the given question, consider x as a variable to find for the entire wall to paint, write all the data and compare the data given with respect to the term asked and hence in the given question we can see that, if \[\dfrac{3}{4}\] of a gallon of paint covers \[\dfrac{2}{5}\] of a wall i.e., we can solve by considering both the values with respect to entire wall.

Complete step-by-step solution:
Let us write the given data:
\[\dfrac{3}{4}\] of a gallon of paint covers = \[\dfrac{2}{5}\] of a wall
How many gallons of paint needed to paint entire wall = \[x\]
Let \[x\] be the entire wall to be painted, hence by considering the given data as
\[\dfrac{3}{4} \div \dfrac{2}{5} = \dfrac{x}{1}\]
Hence, cross multiplying the terms we get:
\[\dfrac{2}{{5x}} = \dfrac{3}{4}\]
\[x = \dfrac{3}{4} \times \dfrac{5}{2}\]
\[x = \dfrac{{15}}{8}\]

Therefore, we need \[\dfrac{{15}}{8}\] gallons or \[1\dfrac{7}{8}\] gallons to paint the entire wall.

Additional information: Gallon is a unit of measurement used for liquids.
Unit Rate: Comparison or ratio between two different quantities with different units. Where one quantity tells how much quantity in one unit. The quantity may be anything. The rate is nothing but the ratio between two quantities.

Note: The key point to solve these types of unit rate sums is that comparing the data with respect to the terms asked i.e., while solving the given question we need to consider the ratios between the whole wall, and consider any variable as entire wall to paint hence by this we can have find out how many gallons is needed to paint the entire wall.