TEKS A.5A Worksheets — Algebra I Solve linear equations in one variable, including

Zara wants to buy a new bicycle that costs $300. She currently has $120 saved. Every week, she saves an additional $30. How many weeks will it take her to save enough money to buy the bicycle?

1. 6 ✓
2. 5
3. 7
4. 8

Why: Zara needs a total of $300 and has $120 saved. The amount she still needs is $300 - $120 = $180. Since she saves $30 each week, the number of weeks it will take her to save the remaining $180 is 180 / 30 = 6 weeks. Therefore, the correct answer is 6.

Carlos is collecting rocks for his geology class project. He has 15 rocks, and he needs to collect a total of 25 rocks to complete his project. How many more rocks does Carlos need to collect?

1. 10 ✓
2. 15
3. 20
4. 5

Why: To find out how many more rocks Carlos needs to collect, subtract the number of rocks he already has from the total he needs. So, 25 - 15 = 10. Therefore, Carlos needs to collect 10 more rocks.

Jamal is organizing a bake sale at his school in Amarillo, Texas, to raise money for a local charity. He sells cookies for $2 each and brownies for $3 each. Last Saturday, he sold a total of 40 baked goods, which earned him $100. If x represents the number of cookies sold and y represents the number of brownies sold, which equation can be used to represent this situation?

1. x + y = 40 and 2x + 3y = 100 ✓
2. 2x + 3y = 40 and x + y = 100
3. x + 3y = 40 and 2x + y = 100
4. 3x + 2y = 40 and x + y = 100

Why: To formulate the equations, we note that the total number of baked goods is 40, so we have x + y = 40. Additionally, the total revenue from the sales of cookies and brownies is $100, leading to the equation 2x + 3y = 100. Therefore, the correct representation of the situation is both equations: x + y = 40 and 2x + 3y = 100.

Antonio is organizing a road trip from Austin to Galveston. He plans to drive his car, which uses 1/4 gallon of gas for every mile traveled. Antonio also decides to take his friend Sebastian, who will contribute $15 towards the gas costs. The total cost of gas for the trip is expected to be $60. Which equation can be used to find the distance (d) in miles that Antonio will travel to Galveston, considering the contribution from Sebastian?

1. d / 4 + 15 = 60
2. d / 4 - 15 = 60
3. d / 4 = 60 - 15 ✓
4. d + 15 = 60 / 4

Why: To find the distance Antonio will travel, we first need to understand that the total gas cost is $60. The equation should represent the relationship between the distance and the gas cost. Since the car uses 1/4 gallon of gas for every mile, the total cost for gas can be represented as (d / 4), where d is the distance traveled. Since Sebastian is contributing $15 towards the cost, we can set up the equation as d / 4 = 60 - 15. This simplifies to d / 4 = 45, which correctly describes the situation.

Zoe wants to buy a new backpack that costs $45. She has a coupon that gives her 20% off the original price. How much will Zoe pay for the backpack after applying the coupon?

1. $36 ✓
2. $39
3. $40
4. $42

Why: To find the final price after applying the 20% discount, first calculate the amount of the discount: 20% of $45 is 0.20 * 45 = $9. Then, subtract the discount from the original price: $45 - $9 = $36. Therefore, Zoe will pay $36 for the backpack.

David is selling homemade tacos at a local fair in Arlington, Texas. He sells his tacos for $3 each and has expenses totaling $150 for ingredients and permits. If he wants to break even, how many tacos does he need to sell? Let x represent the number of tacos sold. Set up and solve the equation: 3x = 150.

1. 50 ✓
2. 30
3. 40
4. 60

Why: To find out how many tacos David needs to sell to break even, we set up the equation 3x = 150. This means that the total revenue from selling x tacos (3 times the number of tacos) must equal his total expenses of $150. To solve for x, divide both sides by 3: x = 150 / 3, which simplifies to x = 50. Therefore, David needs to sell 50 tacos to cover his expenses.

Yusuf is saving money to buy a new laptop that costs $800. He currently has $200 saved and plans to save $50 each week. How many weeks will it take for Yusuf to have enough money to buy the laptop?

1. 12 ✓
2. 10
3. 14
4. 8

Why: To determine how many weeks it will take for Yusuf to save enough money, we first find out how much more he needs. The laptop costs $800 and he has $200 saved, so he needs an additional $800 - $200 = $600. Since he saves $50 each week, we calculate the number of weeks required by dividing the remaining amount by the amount saved each week: 600 / 50 = 12 weeks. Thus, it will take Yusuf 12 weeks to have enough money to buy the laptop.

Carolina is planning a community garden in Austin, Texas. She needs to buy seed packets for vegetables. Each packet of carrots costs $2, while each packet of tomatoes costs $3. If she buys a total of 12 packets and spends exactly $30, how many packets of each type did she buy? Which equation can be used to represent this situation and help determine the number of packets of carrots (c) and tomatoes (t)?

1. c + t = 12 and 2c + 3t = 30 ✓
2. c + t = 30 and 2c + 3t = 12
3. c + t = 2 and 2c + 3t = 12
4. c + t = 12 and 2c + 3t = 12

Why: The correct equations are c + t = 12, which represents the total number of packets bought, and 2c + 3t = 30, which represents the total cost of the packets. To solve this system, you can use substitution or elimination methods.