Word Problems in Algebra and Geometry

In this lesson, Mr. Holcomb covers various applications of linear equations. He skips the first two questions due to their complexity and focuses on examples that better illustrate the concepts. The lesson includes problems on calculating games played, consecutive integers, book pages, number problems, rectangle dimensions, tickets, skateboarding, and triangle similarity. Each example is solved step-by-step, demonstrating the application of linear equations in different scenarios.

Marvin paid a fixed entrance fee and an additional cost per game at an arcade. If he spent a total of $26.25, how many games did he play?

• 15

• 16

• 17

• 18

If the sum of four consecutive integers is -26, what is the smallest integer?

• -6

• -7

• -8

• -9

Maria read 45 pages on Monday, half of the book on Tuesday, and the remaining 72 pages on Wednesday. How many pages are in the book?

• 234

• 220

• 210

• 200

A number increased by five and then divided by two equals 75. What is the original number?

• 155

• 140

• 145

• 150

The sum of 13 and twice a number is seven less than six times the number. What is the number?

• 3

• 6

• 4

• 5

The width of a rectangle is 7 less than twice its length. If the perimeter is 43.6 inches, what is the area?

• 100.12

• 110.12

• 117.12

• 120.12

If 250 tickets were sold over six days with 35 sold on the first day and an equal number on the remaining days, how many tickets were sold each day after the first?

• 40

• 41

• 42

• 43

Jona skateboarded for some minutes on Monday, twice as many on Tuesday, and half the sum of Monday and Tuesday on Wednesday. If she skated for 3 hours in total, how many minutes did she skate on Monday?

• 30

• 35

• 40

• 45

In similar triangles, if AC corresponds to A'C' and BC corresponds to B'C', and AC is 110.3 - x, what is the value of x if the proportion is maintained?

• 3.1

• 3.0

• 3.3

• 3.2

Determine the length of AC if AC = 10.3 - x and x = 3.1 in similar triangles.

• 6.2

• 7.2

• 8.2

• 9.2