# If \frac{2}{3} ton of gravel covers \frac{3}{4} of a driveway, how many tons of gravel are...

## Question:

If {eq}\frac{2}{3} {/eq} ton of gravel covers {eq}\frac{3}{4} {/eq} of a driveway, how many tons of gravel are required to cover the entire driveway?

(a) {eq}\frac{1}{3} {/eq} ton

(b) {eq}\frac{1}{2} {/eq} ton

(c) {eq}\frac{8}{9} {/eq} ton

(d) {eq}\frac{11}{12} {/eq} ton

## Verbal Statement Into the Equation:

We can translate a verbal statement into an equation by using algebraic operations. Here, we use + for "more than", - for "less than, multiplication for "times" etc. We can then solve it using the algebraic operations on both sides of the equation.

Let us assume that the number of tons of gravel that is required to cover the entire driveway = {eq}x {/eq}.

Then according to the problem:

$$\dfrac{3}{4} \text{ of }x = \dfrac{2}{3}\\[0.4cm] \dfrac{3}{4}x = \dfrac{2}{3}\\[0.4cm] \text{Multiplying both sides by }\dfrac{4}{3}\\[0.4cm] x= \dfrac{2}{3} \times \dfrac{4}{3}= \color{blue}{\boxed{\mathbf{\dfrac{8}{9} \text{ tons}}}}$$

Therefore, the answer is {eq}\color{blue}{\boxed{\mathbf{ \text{ (c)}}}} {/eq}.