Standard Form Linear Equations Word Problems

Small bags of apples are $2 each and large bags of oranges are $6 each. A customer spends a total of $28.

If "x" is the number of bags of apples and "y" is the number of bags of oranges, which equation models this?

• 6x + 2y = 28

• 2x + 6y = 28

Yandel is selling concert tickets for his friend's show. Regular tickets cost $35 and VIP tickets cost $50. Yandel's manager told him he needs to sell $1,000 worth of tickets. Which of the following equations could be used to represent the number of regular tickets, x, and VIP tickets, y, Yandel needs to sell to meet the goal?

• 35x - 50y = 1000

• 50x - 35y = 1000

• 50x + 35y = 1000

• 35x + 50y = 1000

Amy wants to buy soda AND pizza for her Halloween party. She has $45 to spend. One case of soda costs $4, and one pizza costs $8. Write an equation that could be used to find a valid combination for as many cases of soda, x, and pizzas, y, as she can afford.

• 8x + 4y = 45

• 4x - 8y = 45

• 12xy = 45

• 4x + 8y = 45

You are selling drinks at the carnival to raise money. You sell lemonade for $2 per cup and orange drinks for $3 per cup. Your sales totaled $240. Let x be the number of cups of lemonade and y be the number of orange drinks.

Write an equation to represent the situation

• 2x - 3y = 240

• 3y - 2x = 240

• 2x + 3y = 240

• 2 + 3 = 240

You are selling drinks at the carnival to raise money. You sell lemonade for $2 per cup and orange drinks for $3 per cup. Your sales totaled $240. Let x be the number of cups of lemonade and y be the number of orange drinks. If you sold 60 cups of lemonade, how many cups of orange drink did you sell?

• 60

• 40

• 10

• 120

A holiday meal costs $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs, including delivery, for x people?

• y = 12.5x + 30

• y = 12.5 + 30

• y = 12.5 + 30x

A man is climbing down from 100 feet high descending 30 feet per minute.

• y = - 30x + 100

• y = 100 + 30x

• y = 100x + 30

• y = 100x - 30

At a pet store, it costs $5 to wash a cat and $7.50 to wash a dog.  Last week, the store made $60 from washing cats and dogs.  If 6 cats were washed, write and solve a linear equation to find how many dogs were washed.

• 2 dogs

• 3 dogs

• 4 dogs

• not enough information

This problem:

• gives you a rate of change (slope) and a starting point (y-intercept)

• relates two different objects

• gives you a rate of change (slope) and a sample point (x,y)

This problem:

• gives you a rate of change (slope) and a starting point (y-intercept)

• relates two different objects

• gives you a rate of change (slope) and a sample point (x,y)