Copyright

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.

Answer and Explanation:

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}.


Learn more about this topic:

Loading...
Solving Word Problems with Algebraic Multiplication Expressions

from 6th-8th Grade Math: Practice & Review

Chapter 32 / Lesson 10
4.3K

Related to this Question

Explore our homework questions and answers library