Chapter 8.7, Problem 37IP

To determine

Find the time Khadijah can spend working on her history project.

Answer to Problem 37IP

  $x+\frac{3}{4}\le 3$; Khadijah can spend at most $2\frac{1}{4}$ hours on her history project?

Explanation of Solution

Given:

Khadijah has at most three hours to work on a math assignment and a history project. If the math assignment will take $\frac{3}{4}$ hour, how much time can Khadijah spend working on her history project?

Concept Used:

Khadijah has at most three hours to work on a math assignment and a history project. If the math assignment will take $\frac{3}{4}$ hour, how much time can Khadijah spend working on her history project?

Khadijah has at most three hours to work, this represents by inequality sign $\le 3$

The math assignment will take $\frac{3}{4}$ hour

Math assignment + History assignment $\le 3$

Let x be represent by the times needed for History project.

The required inequality is $x+\frac{3}{4}\le 3$

Calculation:

The math assignment will take $\frac{3}{4}$ hour

Math assignment + History assignment $\le 3$

Let x be represent by the times needed for History project.

The required inequality is $x+\frac{3}{4}\le 3$

Now solve for x:

  $\begin{array}{l}x+\frac{3}{4}\le 3\\ x+\frac{3}{4}-\frac{3}{4}\le 3-\frac{3}{4}\\ x\le 2\frac{1}{4}\end{array}$ Khadijah can spend at most $2\frac{1}{4}$ hours on her history project?

Thus, Khadijah can spend at most $2\frac{1}{4}$ hours on her history project?