TEKS A.3A Worksheets — Algebra I Determine the slope of a line given

Hudson is organizing a school fundraiser to support wildlife conservation in Texas. He plans to sell packs of snacks and drinks. Each snack pack costs $5, and each drink costs $3. If he sells a total of 60 items and earns $240, how many snack packs did he sell? Set up an equation to find the correct number of snack packs sold.

1. 30 ✓
2. 36
3. 24
4. 20

Why: To find the number of snack packs Hudson sold, let's define the number of snack packs as x and the number of drinks as y. We have two equations based on the problem: x + y = 60 (the total number of items sold) and 5x + 3y = 240 (the total revenue earned). We can solve these equations simultaneously. From the first equation, we can express y as y = 60 - x. We substitute this into the second equation: 5x + 3(60 - x) = 240, which simplifies to 5x + 180 - 3x = 240. Combining like terms gives us 2x + 180 = 240. Subtracting 180 from both sides gives us 2x = 60, and dividing both sides by 2 results in x = 30. Therefore, Hudson sold 30 snack packs.

Sebastian is helping his family at their farm in Nacogdoches, Texas. They are planting two types of crops: corn and tomatoes. The total amount of land they have is 100 acres. They decide to allocate some of the land for corn and the rest for tomatoes. If they plant corn on x acres and tomatoes on (100 - x) acres, and it is known that the corn yields 1500 pounds per acre while the tomatoes yield 1200 pounds per acre, which equation represents the total yield, in pounds, from both crops?

1. 1800x + 120000
2. 1500x + 1200(100 - x) ✓
3. 1200x + 1500(100 - x)
4. 1500x + 1200x

Why: To find the total yield from both crops, we can write an equation that represents the yield of each crop based on the acres planted. The yield for corn is 1500 pounds per acre multiplied by x acres, which gives us 1500x. For tomatoes, the yield is 1200 pounds per acre multiplied by (100 - x) acres, resulting in 1200(100 - x). Thus, the total yield equation is 1500x + 1200(100 - x), which matches choice 2.

Isabella is planning a fundraiser for her school in Waco, Texas, where she sells homemade tamales. If she charges $8 per dozen tamales, and she spends $20 on ingredients, what is the equation that represents her profit (P) as a function of the number of dozen tamales sold (d)?

1. P = 8d - 20 ✓
2. P = 20d + 8
3. P = 20 - 8d
4. P = 8 + 20d

Why: To find the profit equation, we start with the revenue from selling tamales, which is 8d (since she charges $8 per dozen). Then we subtract the cost of the ingredients, which is $20. Therefore, the profit equation is P = 8d - 20, making the correct answer 8d - 20.

Maria is studying the growth of bluebonnet plants in Texas' Hill Country. She collects data over several weeks and records the following information: After 2 weeks, the plants' average height is 6 inches, and after 4 weeks, their average height is 12 inches. If the relationship between the number of weeks (w) and the height of the plants (h) can be expressed as a linear equation in the form h = mw + b, what is the slope (m) of the line that represents the growth of the bluebonnet plants?

1. 3 ✓
2. 2
3. 6
4. 4

Why: To determine the slope (m) of the line, we use the formula for slope, which is m = (change in height) / (change in weeks). From the data, the change in height is 12 inches - 6 inches = 6 inches, and the change in weeks is 4 weeks - 2 weeks = 2 weeks. Therefore, the slope (m) is 6 / 2 = 3. Thus, the correct answer is 3.

Saniya is helping her family run a citrus stand in the Rio Grande Valley. They sell oranges and lemons, where the price of a bag of oranges is $3 and the price of a bag of lemons is $2. If Saniya sells a total of 30 bags of fruit for $80, which equation can be used to find the number of bags of oranges, x, that she sold?

1. 3x + 2(30 - x) = 80 ✓
2. 3x + 2x = 80
3. 3(30 - x) + 2x = 80
4. 3x + 2(30 + x) = 80

Why: To determine the number of bags of oranges Saniya sold, we can set up an equation where x represents the number of bags of oranges sold and (30 - x) represents the number of bags of lemons sold. The total revenue from sales must equal $80. The equation 3x (revenue from oranges) + 2(30 - x) (revenue from lemons) = 80 correctly represents this scenario.

Daniel is studying the impact of the Ogallala Aquifer on local agriculture in Texas. He finds that the water level in the aquifer decreases at a steady rate. If the water level is currently 150 feet and decreases by 5 feet each year, which equation can be used to represent the water level after 't' years?

1. h = 150 - 5t ✓
2. h = 5t - 150
3. h = 150 + 5t
4. h = 150t - 5

Why: The correct equation is h = 150 - 5t. This represents the starting water level of 150 feet and decreases by 5 feet for each year that passes, which is the rate of decrease over time. The other options do not correctly reflect the scenario described.

Andres is planning to build a fence around his backyard in Texas. The cost of the fence materials is represented by the equation C = 20x + 150, where C is the total cost in dollars and x is the length of the fence in feet. What does the slope of this equation represent in this scenario?

1. The total cost of the fence at 0 feet
2. The cost of the fence per foot of length ✓
3. The initial cost of materials without any length
4. The total length of the fence at a cost of $150

Why: The slope of the equation C = 20x + 150 is 20, which represents the cost per foot of the fence materials. This means for every additional foot of fence, the cost increases by $20. Hence, the slope indicates the cost of the fence per foot of length.

Jorge is planting a community garden in Houston. He plans to plant tomatoes and peppers. The total number of plants he will plant is represented by the equation x + y = 20, where x is the number of tomato plants and y is the number of pepper plants. If each tomato plant requires 3 square feet of space and each pepper plant requires 2 square feet, and he has a total of 56 square feet available, which of the following equations correctly represents this situation?

1. 3x + 2y = 56 ✓
2. 3x + 2y = 20
3. x + 3y = 56
4. 2x + y = 20

Why: To find the correct equation representing the space requirements, we set up an equation based on the number of plants: 3 square feet per tomato plant (x) and 2 square feet per pepper plant (y). Therefore, the equation for the area should be 3x + 2y = 56, where the total area is 56 square feet. Consequently, 3x + 2y = 56 is the correct representation of the situation.