TEKS 8.8C Worksheets — Grade 8 Model and solve one-variable equations with variables

Sofia is saving up to buy a new bicycle that costs $240. She has already saved $75 from her allowance. If she saves $15 each week from her chores, how many weeks will it take for her to have enough money to buy the bicycle?

1. 11 ✓
2. 10
3. 12
4. 15

Why: To find out how many more weeks it will take for Sofia to save enough money, first calculate how much more she needs: $240 - $75 = $165. Next, divide the remaining amount by how much she saves each week: $165 ÷ $15 = 11. Therefore, it will take Sofia 11 weeks to save enough money.

Justice is organizing a charity run in Austin to raise money for local schools. The total registration fee for each runner is 20 dollars. Justice has already raised 180 dollars from sponsors. If Justice wants to raise a total of 600 dollars, how many runners does he need to register? Which equation can be used to find the number of runners, r, Justice needs to register?

1. r = (600 - 180) / 20 ✓
2. r = (180 - 600) / 20
3. r = 600 - 20r
4. r = (600 + 180) / 20

Why: To find out how many runners Justice needs to register, we can set up the equation r = (600 - 180) / 20. First, subtract 180 from 600 to get 420. Then, divide 420 by 20 to find that Justice needs 21 runners to meet his goal of 600 dollars.

Emilio is growing a vegetable garden in his backyard in McAllen, Texas. He has a total of 25 square feet for planting. He plans to plant tomatoes and peppers. The area for tomatoes will be represented by the equation 2x + 5 = 3x - 10, where x represents the area in square feet allocated to the tomatoes. How much area will be allocated to the peppers if he uses the remaining space for them?

1. 15
2. 10 ✓
3. 20
4. 5

Why: To find the area allocated for tomatoes, we need to solve the equation 2x + 5 = 3x - 10. First, subtract 2x from both sides: 5 = x - 10. Then, add 10 to both sides to isolate x: 5 + 10 = x, which gives x = 15. Therefore, the area for tomatoes is 15 square feet. To find the area for peppers, subtract the area for tomatoes from the total garden area: 25 - 15 = 10 square feet. So, the area allocated to the peppers is 10 square feet.

Emilio and his family run a pecan farm in Texas. They harvested 150 pounds of pecans this season. Of this total, they sold 2/5 of their harvest at the local market. They also donated 10 pounds of pecans to a local charity. How many pounds of pecans does Emilio have left after these transactions?

1. 80 ✓
2. 70
3. 60
4. 90

Why: To find out how many pounds of pecans Emilio has left, first calculate how many he sold. They sold 2/5 of 150 pounds, which is 150 * (2/5) = 60 pounds. Next, subtract that from the total: 150 - 60 = 90. Then, subtract the 10 pounds donated to charity: 90 - 10 = 80. Therefore, Emilio has 80 pounds left.

Priya is planning a trip to Big Bend National Park with her family. They want to explore the park for 3 days and have allocated a budget of $600 for the trip. If they plan to spend $150 each day on food and activities, how much money will Priya have left after the trip?

1. $150 ✓
2. $300
3. $450
4. $0

Why: To find out how much money Priya will have left after the trip, first calculate the total amount spent on food and activities over 3 days. They plan to spend $150 each day, so for 3 days, it will be 3 * 150 = $450. Now, subtract this amount from their total budget: $600 - $450 = $150. Therefore, Priya will have $150 left after the trip.

Roberto is preparing for the State Fair of Texas, where he plans to sell his famous barbecue brisket. He estimates that each pound of brisket costs him $12 to prepare. He wants to make a total of $240 in profit after selling the brisket. He plans to sell each pound for $18. If he sells x pounds of brisket, which equation best represents the relationship between his costs, sales, and desired profit?

1. 18x - 12x = 240 ✓
2. 18x + 12 = 240
3. 12x + 18 = 240
4. 240 - 12x = 18x

Why: The equation 18x - 12x = 240 represents the profit calculation where the income from selling x pounds of brisket (18x) subtracts the cost of preparing x pounds of brisket (12x), resulting in a profit of $240. This correctly models Roberto's goal of making $240 in profit.

Priya is collecting donations for a local animal shelter. She wants to buy bags of dog food that cost $15 each. If she has already raised $90 and each bag of food costs $15, how many bags can she buy with the money she has raised?

1. 6 ✓
2. 5
3. 7
4. 4

Why: To find out how many bags of dog food Priya can buy, divide the total amount of money she raised by the price of each bag. She raised $90 and each bag costs $15, so you calculate 90 ÷ 15, which equals 6. Therefore, Priya can buy 6 bags of dog food.

Atlas wants to build a small fence around his backyard in San Antonio. The total length of the fence will be 3 times the width of the yard plus a 5-foot gate. If the width of the backyard is represented by the variable w, which of the following equations represents the total length of the fence in feet?

1. L = 3w + 5 ✓
2. L = 3w - 5
3. L = w + 5
4. L = 5 - 3w

Why: To model the total length of the fence, we need to account for both the width of the yard and the gate. If the width is w, then the total length L can be expressed as three times the width plus the length of the gate. Thus, the equation is L = 3w + 5. The other options either misinterpret the relationship or incorrectly apply subtraction instead of addition.