TEKS 8.5I Worksheets — Grade 8 Write an equation in the form y

Daniela is organizing a food booth at the Texas State Fair in Dallas. She plans to sell tacos and drinks. Each taco costs $3.50 and each drink costs $2.00. If she wants to have at least $150 in profit after covering her booth cost of $50, how many tacos and drinks must she sell in total if she sells twice as many tacos as drinks? Which equation models the number of tacos, t, and drinks, d, that she must sell to meet her goal?

1. t + d = 100
2. 3.50t + 2d = 200 ✓
3. 7d = 200
4. 3.50t + 2d = 150

Why: To model the situation, we know that Daniela sells twice as many tacos as drinks, meaning t = 2d. We need to find an equation that satisfies the profit requirement. Her total income from tacos and drinks must be equal to her costs plus her desired profit: 3.50t + 2d = 200. The equation comes from the total profit (150) plus the booth cost (50), leading to a total income of 200. Therefore, the correct equation is 3.50t + 2d = 200.

Maria is planting a garden in her backyard in Austin, Texas. She intends to plant a total of 60 plants, which will consist of tomato plants and peppers. If the number of tomato plants is 2 times the number of pepper plants, which equation can represent the relationship between the number of tomato plants (y) and the number of pepper plants (x)?

1. y = 2x ✓
2. y = x + 2
3. y = 2x + 60
4. y = x/2

Why: To find the equation that represents the relationship between the number of tomato plants and pepper plants, we know that the number of tomato plants (y) is 2 times the number of pepper plants (x). This can be expressed as y = 2x. Therefore, the correct answer is y = 2x.

Hannah is selling oranges at the local farmers market in the Rio Grande Valley. She sells 3 oranges for $2.40. After selling 12 oranges, Hannah decides to record the total revenue she earned in a table. If she continues to sell oranges at the same rate, which equation in the form y = mx + b best models the relationship between the number of oranges sold (x) and the total amount earned in dollars (y) if she has no initial costs or fees?

1. y = 0.80x ✓
2. y = 2.40x
3. y = 3x
4. y = 0.60x + 2.40

Why: To find the equation that models the relationship, we first determine the price per orange. Since 3 oranges cost $2.40, the price for one orange is $2.40 / 3 = $0.80. Therefore, if x is the number of oranges sold, the total revenue y can be expressed as y = 0.80x. This matches the first choice.

Roberto runs a bike rental shop in Austin, Texas. He discovered that for every hour a customer rents a bike, they pay $15. Additionally, there is a one-time registration fee of $30. If y represents the total cost in dollars and x represents the number of hours a bike is rented, which equation models the relationship between y and x?

1. y = 15x + 30 ✓
2. y = 15x - 30
3. y = 30x + 15
4. y = 30x - 15

Why: To model the total cost, we need to account for both the hourly rate and the registration fee. The hourly cost is $15 per hour, represented by 15x, and the one-time fee is $30, represented by +30. Thus, the correct equation is y = 15x + 30.

Cristian went to a local farmers market in Austin, Texas, to buy some fresh peaches. Each peach costs $1.75. Cristian wants to buy a total of 12 peaches. After spending $7.50 on other fruits, he wants to express the total cost of all the peaches he plans to buy using the equation y = mx + b. What is the correct equation that models the total cost of the peaches, where y is the total cost, m is the cost per peach, x is the number of peaches, and b is the initial amount spent on other fruits?

1. y = 1.75x + 7.50 ✓
2. y = 1.75x - 7.50
3. y = 7.50x + 1.75
4. y = 7.50x - 1.75

Why: The correct equation is y = 1.75x + 7.50. Here, m (the cost per peach) is $1.75, x is the number of peaches Cristian buys, and b is the $7.50 he spent on other fruits. Therefore, the total cost for Cristian can be calculated by adding the base amount spent on other fruits to the cost of the peaches.

Ramon is planning a trip to Enchanted Rock with his friends. They plan to hike a total distance of 12 miles. If they hike the first 3/4 of the distance at a steady pace of 2 miles per hour, which equation can be used to find y, the time in hours it takes to hike the remaining distance at a rate of x miles per hour?

1. y = (12 - (3/4) * 12) / x ✓
2. y = (3/4) * 12 + x
3. y = 12 - (3/4) * 12x
4. y = 3/4 * (12 - 12x)

Why: To find the time it takes to hike the remaining distance after completing 3/4 of the total 12 miles, we first calculate the distance already hiked: (3/4) * 12 = 9 miles. The remaining distance is 12 - 9 = 3 miles. To find the time (y) it takes to hike the remaining distance at a speed of x miles per hour, we use the equation y = remaining distance / speed. Therefore, the correct equation is y = (12 - (3/4) * 12) / x.

Nia decided to save money for a new bicycle. She currently has $150 saved. If she saves an additional $25 each week, how much money will she have saved after 4 weeks?

1. $200
2. $250 ✓
3. $150
4. $100

Why: To find out how much Nia will have after 4 weeks, first calculate the total amount she saves in 4 weeks: 25 * 4 = 100. Then, add this to her current savings: 150 + 100 = 250. So, Nia will have $250 after 4 weeks.

Gabriela is organizing a bake sale in Austin, Texas, to raise money for her school's art program. She charges $3 for each cupcake she sells. If she sells 'x' cupcakes, what equation can be used to determine her total revenue 'y' from selling the cupcakes?

1. y = 3x ✓
2. y = x + 3
3. y = 3 + x
4. y = 3x + 5

Why: To find the total revenue 'y' from selling 'x' cupcakes at $3 each, we multiply the number of cupcakes sold (x) by the price per cupcake (3). This gives us the equation y = 3x, which accurately represents Gabriela's total revenue from the sale.