Lesson: Applications of Systems of 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?

Three numbers sum up to 147. The smallest number is half the middle number, which is half the largest number. What are the three numbers?

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.

Three even numbers add up to 108. The smaller is half the larger and the middle number is of the larger. What are the three numbers?

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?

Your roommate, Dina, 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?

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?

Nabil has lemon, orange, and pomegranate trees in his backyard. An orange weighs 8 oz, a lemon 5 oz, and a pomegranate 11 oz. Nabil 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 Nabil pick?

Amira, Rania, and Yasmine weigh 370 lb in total. If Yasmine weighs 20 lb more than Rania, and Amira weighs 1.5 times as much as Rania, how much does each girl weigh?

A clothing shop 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 shop sell?

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 .

Three roommates shared a package of 12 ice cream bars. If Fady ate twice as many ice cream bars as Karim, and Amir ate three less than Fady, how many ice cream bars did each roommate eat?

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?

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?

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?

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.

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?

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?

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?

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.

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?

Students were asked to bring their favourite 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?

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?