Algebra 2: Linear Equations and Inequalities in

Algebra 2: Linear Equations and Inequalities in One Variable
Topic B3: Applications | VERSION A Name: ___________________________________________ 1.
A rectangle is 5 times as long as it is wide. The perimeter is 48 feet. Find the dimensions. 2.
A square has a perimeter of 32 feet. Find the length of each side. 3.
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A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 56 feet. If the material used to build the pen is $1.25 per foot for the longer sides and $2.25 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen. 7.
Shane returned from a trip to Las Vegas with $450, which was 25% more money than he had at the beginning of the trip. How much money did Shane have at the beginning of his trip? 8.
An employee earns $24.70 per hour after receiving a 4% raise. What was the employee's hourly pay before raise? Round your answer to the nearest cent. 9.
According to a milk carton, 2% milk contains 70% less fat than whole milk. The nutrition label on the other side of the carton states that one serving of this milk contains 2.5 grams of fat. How many grams of fat are in an equivalent serving of whole milk? A triangle has a perimeter of 46 inches. The medium side is 4 more than the short side, and the longest side is 4 times the length of the shortest side. Find the shortest side. A triangle has a perimeter of 32 inches. The medium side is 7 more than the short side, and the longest side is 3 times the length of the shortest side. Find the shortest side. A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 88 feet. If the material used to build the pen is $1.75 per foot for the longer sides and $2.50 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen. 10. One angle is 21 less than 2 times another. Find the measure of each angle if: 𝑎. They are complements of each other. 𝑏. They are supplements of each other. www.varsitylearning.com 1 Algebra 2: Linear Equations and Inequalities in One Variable
Topic B3: Applications | VERSION A Name: ___________________________________________ 11. One angle is 25 less than 4 times another. Find the measure of each angle if: 𝑎. They are complements of each other. 𝑏. They are supplements of each other. 12. A triangle is such that the largest angle is 5 times the smallest angle. The third angle is 18 less than the largest angle. Find the measure of each angle. The measure of the smallest angle is degrees, the medium angle is degrees, and the measure of the largest angle is degrees. 16. A person makes an overseas phone call. The telephone company charges 83 cents for the first minute and then 93 cents for each minute thereafter. Because it's an overseas phone call, there is also a 75 cent service charge. If the phone call cost $20.18, how many minutes did this person talk? 17. A boat that can travel 15 miles per hour in still water is traveling along a stream with a current of 2 miles per hour. The distance the boat will travel upstream is given by the formula 𝑑 = 𝑟 − 𝑐 ⋅ 𝑡, and the distance it will travel downstream is given by the formula 𝑑 = 𝑟 + 𝑐 ⋅ 𝑡. Use these formulas with 𝑟 = 15 and 𝑐 = 2 to complete the following table. 13. A triangle is such that the largest angle is 12 times the smallest angle. The third angle is 20 less than the largest angle. Find the measure of each angle. The measure of the smallest angle is degrees, the medium angle is degrees, and the measure of the largest angle is degrees. 14. A woman has a total of $12,000 to invest. She invests part of the money in an account that pays 9% per year and the rest in an account that pays 10% per year. If the interest earned in the first year is $1,110, how much did she invest in each account? Time (hours) Distance Upstream (miles) Distance Downstream (miles) 1 2 3 4 5 6 18. A farmer buys 62 feet of fencing material to build a rectangular livestock pen. Fill in the second column of the table to find the length of the pen if the width is 4, 6, 8, 10, or 12 feet. Then find the area of each of the pens formed. 15. Tickets for a school event were $2.75 for students and $3.50 for parents. If a total of 89 tickets were sold for $283.00, how many student and parent tickets were sold? Width (ft.) Length (ft.) Area (ft.2) 4 6 8 10 12 www.varsitylearning.com 2 Algebra 2: Linear Equations and Inequalities in One Variable
Topic B3: Applications | VERSION A Name: ___________________________________________ 1.
A rectangle is 5 times as long as it is wide. The perimeter is 48 feet. Find the dimensions. 20 ft. x 4 ft. 2.
A square has a perimeter of 32 feet. Find the length of each side. 8 ft. 3.
4.
5.
A triangle has a perimeter of 46 inches. The medium side is 4 more than the short side, and the longest side is 4 times the length of the shortest side. Find the shortest side. 7 in. A triangle has a perimeter of 32 inches. The medium side is 7 more than the short side, and the longest side is 3 times the length of the shortest side. Find the shortest side. 5 in. A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 88 feet. If the material used to build the pen is $1.75 per foot for the longer sides and $2.50 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen. $170.50 6.
A livestock pen is built in the shape of a rectangle that is 3 times as long as it is wide. The perimeter is 56 feet. If the material used to build the pen is $1.25 per foot for the longer sides and $2.25 per foot for the shorter sides (the shorter sides have gates, which increase the cost per foot), find the cost to build the pen. $84.00 7.
Shane returned from a trip to Las Vegas with $450, which was 25% more money than he had at the beginning of the trip. How much money did Shane have at the beginning of his trip? $360 8.
An employee earns $24.70 per hour after receiving a 4% raise. What was the employee's hourly pay before raise? Round your answer to the nearest cent. $23.75 9.
According to a milk carton, 2% milk contains 70% less fat than whole milk. The nutrition label on the other side of the carton states that one serving of this milk contains 2.5 grams of fat. How many grams of fat are in an equivalent serving of whole milk? 8.33 grams of fat 10. One angle is 21 less than 2 times another. Find the measure of each angle if: 𝑎. They are complements of each other. 37∘ and 53∘ 𝑏. They are supplements of each other. 67∘ and 113∘ www.varsitylearning.com 3 Algebra 2: Linear Equations and Inequalities in One Variable
Topic B3: Applications | VERSION A Name: ___________________________________________ 11. One angle is 25 less than 4 times another. Find the measure of each angle if: 𝑎. They are complements of each other. 23∘ and 67∘ 𝑏. They are supplements of each other. 41∘ and 139∘ 12. A triangle is such that the largest angle is 5 times the smallest angle. The third angle is 18 less than the largest angle. Find the measure of each angle. The measure of the smallest angle is 18 degrees, the medium angle is 72 degrees, and the measure of the largest angle is 90 degrees. 16. A person makes an overseas phone call. The telephone company charges 83 cents for the first minute and then 93 cents for each minute thereafter. Because it's an overseas phone call, there is also a 75 cent service charge. If the phone call cost $20.18, how many minutes did this person talk? 21 min. 17. A boat that can travel 15 miles per hour in still water is traveling along a stream with a current of 2 miles per hour. The distance the boat will travel upstream is given by the formula 𝑑 = 𝑟 − 𝑐 ⋅ 𝑡, and the distance it will travel downstream is given by the formula 𝑑 = 𝑟 + 𝑐 ⋅ 𝑡. Use these formulas with 𝑟 = 15 and 𝑐 = 2 to complete the following table. 13. A triangle is such that the largest angle is 12 times the smallest angle. The third angle is 20 less than the largest angle. Find the measure of each angle. The measure of the smallest angle is 8 degrees, the medium angle is 76 degrees, and the measure of the largest angle is 96 degrees. 14. A woman has a total of $12,000 to invest. She invests part of the money in an account that pays 9% per year and the rest in an account that pays 10% per year. If the interest earned in the first year is $1,110, how much did she invest in each account? $9,000 in the first account, and $3,000 in the second account Time (hours) Distance Upstream (miles) Distance Downstream (miles) 1 13 17 2 26 34 3 39 51 4 52 68 5 65 85 6 78 102 18. A farmer buys 62 feet of fencing material to build a rectangular livestock pen. Fill in the second column of the table to find the length of the pen if the width is 4, 6, 8, 10, or 12 feet. Then find the area of each of the pens formed. 15. Tickets for a school event were $2.75 for students and $3.50 for parents. If a total of 89 tickets were sold for $283.00, how many student and parent tickets were sold? Students: 38 tickets; Parents: 51 tickets Width (ft.) Length (ft.) Area (ft.2) 4 27 108 6 25 150 8 23 184 10 21 210 12 19 228 www.varsitylearning.com 4