Worksheet: Applications of Systems of Equations in Three Variables
In this worksheet, we will practice solving real-world problems using a system of linear equations in three variables.
An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than half the number of cats, and there are 20 more cats than dogs, how many of each are at the shelter?
- A70 rabbits, 150 cats, 130 dogs
- B78 rabbits, 146 cats, 126 dogs
- C180 rabbits, 95 cats, 75 dogs
- D120 rabbits, 125 cats, 105 dogs
At a market, strawberries, oranges, and kiwis make up of the total fruit sold. Twice as many strawberries are sold than oranges, and kiwis sell one more percentage point than oranges. For each fruit, find the percentage of total fruit sold.
- Astrawberries: , oranges: , kiwi:
- Bstrawberries: , oranges: , kiwi:
- Cstrawberries: , oranges: , kiwi:
- Dstrawberries: , oranges: , kiwi:
If the measure of one angle of a triangle is half the measure of the second angle and less than the measure of the third one by , then what are the measures of the three angles?
400 pets were entered into a pet shelter for dogs, cats, and rabbits. There were twice as many cats as rabbits, and 50 more dogs than cats. How many of each type of pet were there?
- A190 dogs, 70 cats, 140 rabbits
- B138 dogs, 87 cats, 175 rabbits
- C138 dogs, 175 cats, 87 rabbits
- D190 dogs, 140 cats, 70 rabbits
Your roommate, Amelia, offered to buy groceries for you and your other roommate. The total bill was $82. She forgot to keep the receipts but remembered that your groceries were $0.05 cheaper than half of her groceries and that your other roommate’s groceries were $2.10 more than your groceries. How much was each person's share of the groceries?
- Amy share: $33.63, Amelia’s share: $16.84, other roommate’s share: $31.53
- Bmy share: $19.95, Amelia’s share: $40, other roommate’s share: $22.05
- Cmy share: $20, Amelia’s share: $39.90, other roommate’s share: $22.10
- Dmy share: $21, Amelia’s share: $42.10, other roommate’s share: $18.90
In a bag, a child has 325 coins worth $19.50. There are three types of coins: pennies, nickels, and dimes. If the bag contains the same number of nickels as dimes, how many of each type of coin are in the bag?
- A105 pennies, 110 nickles, 110 dimes
- B75 pennies, 125 nickles, 125 dimes
- C25 pennies, 150 nickles, 150 dimes
- D315 pennies, 5 nickles, 5 dimes
William has lemon, orange, and pomegranate trees in his backyard. An orange weighs 8 oz, a lemon 5 oz, and a pomegranate 11 oz. William picked 142 pieces of fruit weighing a total of 70 lb 10 oz. Given that he picked 15.5 times more oranges than pomegranates, how many of each of the three fruits did William pick?
- A124 oranges, 10 lemons, 8 pomegranates
- B110 oranges, 25 lemons, 7 pomegranates
- C93 oranges, 43 lemons, 6 pomegranates
- D100 oranges, 20 lemons, 22 pomegranates
Sophia, Hannah, and Natalie weigh 370 lb in total. If Natalie weighs 20 lb more than Hannah, and Sophia weighs 1.5 times as much as Hannah, how much does each girl weigh?
- ASophia’s weight is 120 lb, Hannah’s weight is 80 lb, Natalie’s weight is 170 lb
- BSophia’s weight is 150 lb, Hannah’s weight is 100 lb, Natalie’s weight is 120 lb
- CSophia’s weight is 100 lb, Hannah’s weight is 150 lb, Natalie’s weight is 120 lb
- DSophia’s weight is 150 lb, Hannah’s weight is 120 lb, Natalie’s weight is 100 lb
A clothing store has three different types of hats for sale: straw hats, beanies, and cowboy hats. The straw hat is priced at $13.99, the beanie at $7.99, and the cowboy hat at $14.49. If 100 hats were sold this past quarter, was taken in by sales, and the amount of beanies sold was 10 more than cowboy hats, how many of each did the clothing store sell?
- A30 straw hats, 40 beanies, 30 cowboy hats
- B20 straw hats, 45 beanies, 35 cowboy hats
- C5 straw hats, 55 beanies, 40 cowboy hats
- D10 straw hats, 50 beanies, 40 cowboy hats
Using the following facts, is it possible to calculate the annual salaries of the three workers? Why?
- The sum of the annual salaries of the warehouse manager and the office manager is .
- The office manager makes more than the truck driver annually.
- The annual salaries of the warehouse manager and the truck driver total .
- A Yes, because the system is independent.
- B There are no solutions.
- CNo, because there are infinitely many solutions.
Three roommates shared a package of 12 ice cream bars. If Michael ate twice as many ice cream bars as David, and Liam ate three less than Michael, how many ice cream bars did each roommate eat?
- AMichael: 5, David: 5, and Liam: 2
- BMichael: 4, David: 5, and Liam: 3
- CMichael: 6, David: 3, and Liam: 3
- DMichael: 4, David: 2, and Liam: 6
A bag of mixed nuts contains cashews, pistachios, and almonds. There are nuts in the bag in total, and there are 100 fewer almonds than pistachios. Each cashew weighs 3 grams, each pistachio weigh 4 grams, and each almond weighs 5 grams. If the bag weighs 3.7 kg, how many of each nut are in the bag?
- A200 almonds, 500 cashews, 300 pistachios
- B400 almonds, 100 cashews, 500 pistachios
- C300 almonds, 500 cashews, 200 pistachios
- D300 almonds, 300 cashews, 400 pistachios
A movie theater sold tickets for three different movies at three different prices: $5 for the first movie, $11 for the second movie, and $12 for the third movie. 100 tickets were sold for the first movie. The total number of tickets sold was 642, for a total revenue of $6 774. How many tickets were sold for each movie?
- A100 for the first movie, 200 for the second movie, and 342 for the third movie
- B100 for the first movie, 312 for the second movie, and 230 for the third movie
- C100 for the first movie, 230 for the second movie, and 312 for the third movie
- D100 for the first movie, 342 for the second movie, and 200 for the third movie
At one time, in the United States, of the 398 species on the endangered species list were either mammals, birds, or fish. Birds accounted for 0.7 more than fish, and fish accounted for 1.5 more than mammals. What were the percentages of the endangered mammals, birds, and fish?
- Amammals: , birds: , fish:
- Bmammals: , birds: , fish:
- Cmammals: , birds: , fish:
- Dmammals: , birds: , fish:
Last year, at a women's prison, the total number of inmates aged 20–49 totaled . This year, the 20–29 age group increased by 10, the 30–39 age group decreased by 20, and the 40–49 age group doubled. There are now prisoners. Originally, there were 500 more in the 30–39 age group than in the 20–29 age group. Determine the prison population for each age group last year.
- AThe 20–29 age group: , the 30–39 age group: 825, the 40–49 age group:
- BThe 20–29 age group: 825, the 30–39 age group: , the 40–49 age group:
- CThe 20–29 age group: , the 30–39 age group: , the 40–49 age group: 825
- DThe 20–29 age group: , the 30–39 age group: , the 40–49 age group: 825
The top three countries in oil production in a certain year were Saudi Arabia, the United States, and Russia. Together they produced of the world’s produced oil. Saudi Arabia and the United States combined produced of the world’s production, and Saudi Arabia produced more oil than Russia. What percent of the world’s oil production did each of these countries produce?
- ASaudi Arabia: , US: , Russia:
- BSaudi Arabia: , US: , Russia:
- CSaudi Arabia: , US: , Russia:
- DSaudi Arabia: , US: , Russia:
The top three oil-producing regions in the United States in a certain year were the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for of the United States oil production. The Gulf of Mexico and Texas combined were responsible for of oil production. Texas produced 3 percentage more than Alaska. What percent of United States oil production came from each of the three regions?
- AGulf of Mexico = , Texas = , Alaska =
- BGulf of Mexico = , Texas = , Alaska =
- CGulf of Mexico = , Texas = , Alaska =
- DGulf of Mexico = , Texas = , Alaska =
Meat consumption in the United States can be broken into three categories: red meat, poultry, and fish. If fish makes up 5 percentage points less than one-quarter of poultry consumption, and red meat consumption is 20.85 percentage points higher than poultry consumption, what are the percentages of meat consumption?
- Ared meat: , poultry: , fish:
- Bred meat: , poultry: , fish:
- Cred meat: , poultry: , fish:
- Dred meat: , poultry: , fish:
At an ice cream shop, three flavors are increasing in demand. Last year, banana, pumpkin, and rocky road ice cream made up of total ice cream sales. This year, the same three ice creams made up of total sales. The rocky road sales doubled, the banana sales increased by , and the pumpkin sales increased by .
If the rocky road ice cream had one percentage point fewer sales than the banana ice cream last year, find out the percentage of total ice cream sales each individual ice cream achieved last year.
- Abanana: , pumpkin: , rocky road :
- Bbanana: , pumpkin: , rocky road:
- Cbanana: , pumpkin: , rocky road:
- Dbanana: , pumpkin: , rocky road:
The top three countries in oil consumption in a certain year were the United States, Japan, and China. Together they consumed of the world’s consumed oil. The United States consumed more than four times China’s consumption. The United States also consumed more than triple Japan’s consumption. What percent of the world’s oil consumption did each of these countries consume?
- AUS: , China: , Japan:
- BUS: , China: , Japan:
- CUS: , China: , Japan:
- DUS: , China: , Japan:
Students were asked to bring their favorite fruit to class. of the fruits consisted of bananas, apples, and oranges. Oranges were twice as popular as bananas, and apples were less popular than bananas. What percentage of the total fruit was each type?
- A oranges, bananas, apples
- B oranges, bananas, apples
- C oranges, bananas, apples
- D oranges, bananas, apples
In one year, the top three sources of oil imports for the United States were Saudi Arabia, Mexico, and Canada. These three countries accounted for of the total oil imports. The United States imported more from Saudi Arabia than they did from Mexico and more from Saudi Arabia than they did from Canada. What percent of the total United States oil imports did each of these countries supply?
- ASaudi Arabia: , Mexico: , Canada:
- BSaudi Arabia: , Mexico: , Canada:
- CSaudi Arabia: , Mexico: , Canada:
- DSaudi Arabia: , Mexico: , Canada:
A farmer constructed a chicken coop out of chicken wire, wood, and plywood. The chicken wire cost $2 per square foot, the wood $10 per square foot, and the plywood $5 per square foot. Overall, the farmer spent $51 on 14 square feet of materials. Given that he used 3 square feet more chicken wire than plywood, how much of each material did the farmer use?
- Achicken wire: 8 ft2, plywood: 5 ft2, wood: 1 ft2
- Bchicken wire: 5 ft2, plywood: 2 ft2, wood: 7 ft2
- Cchicken wire: 7 ft2, plywood: 4 ft2, wood: 3 ft2
- Dchicken wire: 6 ft2, plywood: 3 ft2, wood: 5 ft2