Standard Form of Linear Equation Word Problem

Priya is planning a movie night at her place and wants to buy popcorn AND pizza for her friends Luna and Noah. She has $45 to spend. One bag of popcorn costs $4, and one pizza costs $8. Write an equation that could be used to find a valid combination for as many bags of popcorn, x, and pizzas, y, as she can afford.

• 8x + 4y = 45

• 4x - 8y = 45

• 12xy = 45

• 4x + 8y = 45

Harper, Anika, and Aiden were volunteering at a local basketball game. The tickets were priced at $5 for students (x) and $7 for adults (y). If they managed to collect $500 from ticket sales, write an equation that represents this scenario.

• 7x+5y=500

• y=7x+500

• 5x+7y=500

• y=500x+7

Michael, Emma, and Ava are helping Dalyn sell girl scout cookies at a local fair. Dalyn sold 7 boxes of thin mints (x) and 12 boxes of tagalongs (y). If they collectively made $82 selling cookies, write an equation that represents the scenario.

• 7x+12y=82

• 12x+7y=82

• 7x+82y=7

• y=7x+82

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

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

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

A football team scores 63 points. All of the points come from field goals (x) worth 3 points and touchdowns (y) worth 7 points. Write an equation in standard form that represents this situation. Then convert it to slope-intercept form. Select the correct standard form and slope-intercept form.

• 3x + 7y = 63

• 7x + 3y = 63

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)

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

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)