121ExerciseSet2.5
Chapter2: ElementaryandIntermediateAlgebra:GraphsandModels
51. Familiarize. Let N = the number of times the cricket chirps per minute. Let T = the corresponding Fahrenheit temperature. Translate. We are already given the equation relating Fahrenheit temperature T, in degrees, and the number of times a cricket chirps per minute N. We are to determine the number of chips corresponding to 80°F. 40 more than one fourth Temperature is the number of chirps. T N 4 40 Carry out. We substitute 80 for T and solve the equation for N. T 1N 40 4 1 80 N 40 Substituting 80 for T 4 1
40
1
N 4
160 N
Subtracting 40
121
200-m dash is 0.028 100 20.8 , or 18 sec. This result checks. State. The number of years after 1920 is 100, or 1920 100 2020 . 53. Familiarize. We examine the table to determine the size of aquarium and the recommended stocking density. We notice that: 100 = 20 5 120 = 24 5 200 = 40 5 250 = 50 5 This leads us to conclude that size of aquarium is 5 times the stocking density. We let x = the stocking density and we let S = the size of the aquarium. Translate. Size of Aquarium is 5 times the stocking density.
Multiplying by 4
Check If a cricket chirps 160 times per minute, then the Fahrenheit temperature would be 1 160 40 , or 40 + 40, or 80°F. 4 This result checks. State. The number of chirps per minute corresponding to 80°F is 160. 52. Familiarize. Let t = the number of years since 1920. Let R = the number of seconds to complete the 200-m dash. Translate. We are already given the equation relating the number of seconds required R to complete the 200-m dash and time t, the number of years after 1920. 20.8 more than 0.28 Time to run the is times the number of 100-m dash years after 1920. R 0.028t 20.8 Carry out. We substitute 18.0 for R and solve the equation for t. R 0.028t 20.8 18.0 0.028t 20.8 Substituting 18.0 for R
S 5 x Carry out. We substitute 30 in. for x and solve for S. S 5x S 5(30) Substituting 30 for x S 150 Simplify Check. If the aquarium is 150 gallons, then the recommended stocking density 150 5 , or 30 inches. This result checks. State. The aquarium size for 30 in. of fish is 150 gallons. 54. Familiarize. We examine the table to determine the relationship between the cost of an order before shipping and the cost including shipping. Examining each row in the table, we see that the cost including shipping can be determined by adding $5.95 to the cost before shipping: $15.50 + $5.95 = $21.45 . . . . . $21.65 + $5.95 = $27.60 We let T = the cost including shipping and let c = the cost before shipping. Translate.