Interpret Equations

At 0 °C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by 2/25 .

The equation V = 2/25T + 22 represents this situation.

Interpret the meaning of the solution (25, 24)

• When the temperature of the gas is 25° C, its volume is 24 liters.

• After 25 minutes, the volume of the gas is 24 liters.

• At 25 liters, the temperature of the gas is 25°C.

• As the temperature of the gas increases, the volume of the gas increases.

According to Dolbear’s law, you can predict the temperature T (in degrees Fahrenheit) by counting the number x of chirps made by a snowy tree cricket in 1 minute. For each rise in temperature of 0.25°F, the cricket makes an additional chirp each minute.

Interpret the meaning of the solution (40, 50)

• A cricket chirps 40 times in 1 minute when the temperature is 50°F.

• A cricket chirps 50 times in 1 minute when the temperature is 40°F.

• As the temperature increases, the number of chirps increases.

• As the number of chirps increases, the temperature increases.

You water the plants in your classroom at a constant rate. After 5 seconds, your watering can contains 58 ounces of water. Fifteen seconds later, the can contains 28 ounces of water.

The equation y = -2x + 68 represents this situation.

Interpret the meaning of the y-intercept.

• There were 68 ounces of water in your watering can before you started watering your plants.

• You have enough water in your watering can to water 68 plants.

• When you water your plants at a constant rate, it takes 68 seconds for you to run out of water.

• Each plant gets 68 ounces of water.

You buy 8 hostas and 15 daylilies for $193. Your friend buys 3 hostas and 12 daylilies for $117.

The system 8x + 15y = 193 and 3x + 12y = 117 represents this situation.

When graphed, these lines intersect at (11, 7). What is the meaning of this point?

• Each hosta costs $11and each daylily costs $7.

• Each daylily costs $11and each hosta costs $7.

• You and your friend will have the same cost if you both buy 11 hostas and 7 daylilies.

• You and your friend bought a total of 11 hostas and 7 daylilies.

There are 340 calories in 2 cups of cereal with 1 cup of milk. There are 570 calories in 3 cups of the cereal with 2 cups of milk.

The system 2x + y = 340 and 3x + 2y = 570 represents this situation.

Explain the meaning of both variables in the system.

• x represents the cups of cereal

  y represents the cups of milk

• x represents the cups of milk

  y represents the cups of cereal

• x represents the calories in one cup of cereal

  y represents the calories in one cup of milk

• x represents the calories in one cup of milk

  y represents the calories in one cup of cereal

You have $150 to spend on video games.

The inequality 7x + 32y ≤ 150 represents the number x of used video games and the number y of new video games that you can purchase.

Interpret the meaning of the "7" in this inequality.

• Each used video game costs $7.

• Each new video game costs $7.

• You buy 7 used video games.

• You buy 7 new video games.

You are selling newspapers x and magazines y for a school fundraiser. If you sell enough newspapers and magazines, you earn a special school lunch.

The inequality 9x + 5y ≥ 60 represents this situation.

Interpret the meaning of the "60".

• You must at least $60 worth of newspapers and magazines to earn the special lunch.

• You must at least 60 newspapers and magazines to earn the special lunch.

• You have $60 to spend on newspapers and magazines.

• You have 60 newspapers and magazines to sell.

You can spend at most $9 on potatoes and carrots for stew. Potatoes cost $3 per pound, and carrots cost $1.50 per pound.

This situation is shown in the graph.

Explain the meaning of the x-intercept.

• If you don't buy any carrots, you can afford exactly 3 pounds of potatoes.

• If you don't buy any potatoes, you can afford exactly 3 pounds of carrots.

• Potatoes cost $3 per pound.

• The stew recipe needs 3 pounds of potatoes.

You can spend at most $24 at the fair. Game tickets cost $2 each, and ride tickets cost $4 each. You want to buy at least 3 game tickets and more than 2 ride tickets.

The system 2x + 4y < 24, x > 3, and y > 2 represents this situation.

Explain the meaning of each variable.

• x represents the number of game tickets purchased

  y represents the number of ride tickets purchased

• x represents the number of ride tickets purchased

  y represents the number of game tickets purchased

• x represents the cost of game tickets

  y represents the cost of ride tickets

• x represents the cost of ride tickets

  y represents the cost of game tickets

You have at most $60 to spend on trophies and medals to give as prizes for a contest. Trophies cost $12 each and medals cost $3 each. You need to purchase at least 6 prizes.

This situation is represented by the graph.

What does the point (0, 20) represent?

• If you don't buy any trophies, you have enough money to buy 20 medals.

• If you don't buy any medals, you have enough money to buy 20 trophies.

• Even though you only need to buy at least 6 prizes you have enough money to buy 20 prizes.

• If you buy 20 medals, you still have money left to buy trophies.