TEKS 7.11A Worksheets — Grade 7 Model and solve one-variable, two-step equations and

Diego is saving money to buy a new skateboard that costs $150. He already has $45 saved. If he saves $25 each week, how many weeks will it take him to have enough money to buy the skateboard?

1. 4
2. 5 ✓
3. 6
4. 7

Why: To find out how many weeks it will take Diego to save enough money, we first need to calculate how much more he needs. He needs $150 - $45 = $105 more. Since he saves $25 each week, we can divide the amount he needs by how much he saves each week: $105 ÷ $25 = 4.2 weeks. Since he can't save for a fraction of a week, he needs to round up to the next whole week, which means it will take him 5 weeks to have enough money.

Sofia is organizing a neighborhood recycling event in Austin, Texas. She wants to encourage families to bring their aluminum cans to recycle. If each family brings 6 cans, and Sofia has already collected 3 cans from her home, she needs a total of 45 cans for the event. Which equation can be used to find the number of families (f) that need to participate in order for Sofia to reach her goal?

1. 6f + 3 = 45 ✓
2. 6f - 3 = 45
3. 6f + 3 = 42
4. 6f - 6 = 45

Why: To find the number of families that need to participate, we start with the total cans needed (45) and account for the 3 cans Sofia has already collected. This leads to the equation 6f + 3 = 45. To solve for f, we first subtract 3 from both sides to get 6f = 42. Then, dividing by 6 gives us f = 7. Thus, 6f + 3 = 45 correctly represents the situation.

Carlos wants to buy a new bicycle that costs $240. He has saved $80 so far. If he saves $20 each week from his allowance, how many weeks will it take Carlos to have enough money to buy the bicycle?

1. 8 ✓
2. 12
3. 10
4. 6

Why: To find out how many weeks it will take Carlos to save enough money for the bicycle, first determine how much more money he needs. He needs $240 total and has saved $80, so he needs $240 - $80 = $160 more. Since he saves $20 each week, you can find how many weeks it will take by dividing the amount needed by the amount saved each week: 160 / 20 = 8. Therefore, it will take Carlos 8 weeks to save enough money.

Stella is planning a school fundraiser to sell oranges from the Rio Grande Valley. She has a budget of $60 to spend on buying boxes of oranges. Each box costs $15, and she also needs to buy supplies for $24. Which inequality can be used to find the maximum number of boxes of oranges, x, that Stella can purchase while staying within her budget?

1. 15x + 24 ≤ 60 ✓
2. 15x + 24 < 60
3. 15x - 24 ≤ 60
4. 15x + 24 ≥ 60

Why: Stella's total cost includes the cost of the boxes of oranges (15x) plus the supplies ($24). To ensure she does not exceed her budget of $60, the inequality must express that her total spending is less than or equal to $60. Thus, the correct inequality is 15x + 24 ≤ 60.

Mateo loves making salsa with fresh ingredients from his garden. He harvested 3/4 of a pound of tomatoes and 1/2 of a pound of onions. Mateo plans to use 2/3 of the tomatoes and 1/4 of the onions for his salsa recipe. How much of each ingredient will Mateo use for his salsa?

1. 1/2 pound of tomatoes and 1/8 pound of onions ✓
2. 1/4 pound of tomatoes and 1/4 pound of onions
3. 1/2 pound of tomatoes and 1/4 pound of onions
4. 1/3 pound of tomatoes and 1/2 pound of onions

Why: To find how much of each ingredient Mateo will use, we first calculate the quantities. For tomatoes, 2/3 of 3/4 is (2/3) * (3/4) = 6/12 = 1/2 pound. For onions, 1/4 of 1/2 is (1/4) * (1/2) = 1/8 pound. Therefore, Mateo will use 1/2 pound of tomatoes and 1/8 pound of onions for his salsa.

Camille is planting a garden in her backyard in Texas. She plans to plant tomatoes and peppers. Each tomato plant requires 2.5 square feet of space and each pepper plant requires 1.5 square feet of space. If Camille has a total of 30 square feet available for planting and wants to plant the same number of tomato and pepper plants, how many of each type of plant can she plant? Let x represent the number of each type of plant. Which equation can be used to determine the number of plants Camille can plant?

1. 2.5x + 1.5x = 30 ✓
2. 2.5x + 1.5x = 15
3. 2.5x - 1.5x = 30
4. 2.5x + 1.5 = 30

Why: To find out how many tomato and pepper plants Camille can plant, we set up the equation based on the total space available. The total space needed for x tomato plants and x pepper plants can be expressed as 2.5x + 1.5x = 30. Simplifying the equation gives 4x = 30, leading to x = 7.5. Since she cannot plant half a plant, she would need to adjust her numbers, but the correct equation to start with is 2.5x + 1.5x = 30.

Zara is saving for a new laptop that costs $800. She currently has $250 saved. If she saves $50 each week, how many weeks will it take her to have enough money to buy the laptop?

1. 11 ✓
2. 10
3. 12
4. 9

Why: To find out how many more weeks Zara needs to save, first subtract the amount she has from the total cost of the laptop: $800 - $250 = $550. Then, divide the remaining amount by the amount she saves each week: $550 / $50 = 11. Therefore, it will take Zara 11 weeks to save enough money for the laptop.

Emilio is helping his grandmother prepare for a family gathering in Austin, Texas. They plan to make enchiladas that require 3 cups of cheese for every 2 batches. If they want to make 5 batches of enchiladas, how many cups of cheese will they need in total?

1. 10
2. 7.5 ✓
3. 15
4. 12

Why: To find the total amount of cheese needed, first determine how many cups are needed for 5 batches. Since 2 batches require 3 cups of cheese, 1 batch will require 3/2 cups of cheese. For 5 batches, multiply 5 by 3/2 (which is 5 * 1.5) to get 7.5 cups of cheese. Therefore, the correct answer is 7.5.