Accuplacer Models and Applications — practice questions

1. A variable cost is multiplied by the unknown quantity, so it changes as that quantity changes. 2. The 10 cents a mile is multiplied by the miles driven, so it is the variable cost. 3. The 50 dollars a day does not depend on the miles at all, so it is added on as a fixed cost. 4. The model is therefore total cost equal to 0.10 times miles plus 50. _Source: OpenStax College Algebra (CC BY 4.0), section 2.3 Models and Applications_

1. Let W stand for the width, so the length is 2W plus 5. 2. The perimeter formula is 2 times the length plus 2 times the width. 3. Substituting gives 70 equal to 2 times the quantity 2W plus 5, plus 2W. 4. Expanding gives 70 equal to 4W plus 10 plus 2W, so 70 equal to 6W plus 10. 5. Subtracting 10 gives 60 equal to 6W, so the width is 10 feet. 6. The length is then 2 times 10 plus 5, which is 25 feet. 7. Area is length times width, so 25 times 10 gives 250 square feet. 8. The answer 300 square feet uses a length of 30, which comes from doubling the perimeter step wrongly. 9. The answer 175 square feet uses a width of 7, which ignores the added 5 in the length. 10. The answer 120 square feet multiplies the width by the perimeter fraction rather than by the length. _Source: OpenStax College Algebra (CC BY 4.0), section 2.3 Models and Applications_