TEKS 6.4A Worksheets — Grade 6 Compare two rules verbally, numerically, graphically, and

Caroline is studying the cotton fields in the Texas Panhandle for her science project. She learns that for every 3 acres of cotton planted, a farmer can expect to produce 1200 pounds of cotton. If Caroline's father has planted 15 acres, how many pounds of cotton can Caroline expect him to produce? Which expression best represents the total amount of cotton produced?

1. 4000 pounds
2. 6000 pounds ✓
3. 5000 pounds
4. 8000 pounds

Why: To find out how many pounds of cotton Caroline's father can expect to produce, we first determine how many sets of 3 acres are in 15 acres. Since 15 divided by 3 equals 5, we have 5 sets of 3 acres. Each set yields 1200 pounds, so we calculate 5 * 1200, which equals 6000 pounds of cotton. Therefore, the correct answer is 6000 pounds.

Layla is organizing a BBQ event in Houston, Texas. She plans to serve chicken and brisket. For the chicken, she expects to cook 3 pounds for every 2 pounds of brisket. If Layla buys 12 pounds of chicken, how many pounds of brisket will she need to buy to maintain this ratio?

1. 8 pounds ✓
2. 6 pounds
3. 9 pounds
4. 10 pounds

Why: To find the amount of brisket Layla needs, first set up the ratio of chicken to brisket, which is 3/2. If she has 12 pounds of chicken, we can set up a proportion: 3/2 = 12/x, where x is the pounds of brisket. Cross-multiplying gives 3x = 24, so x = 24/3 = 8. Therefore, she needs to buy 8 pounds of brisket to maintain the ratio.

Emma is planning a community garden in Fort Worth, Texas. She wants to plant tomatoes and bell peppers. The ratio of tomato plants to bell pepper plants is 3:4. If she plants a total of 28 plants, how many of each type of plant does she have?

1. 12 tomatoes and 16 bell peppers ✓
2. 15 tomatoes and 13 bell peppers
3. 10 tomatoes and 18 bell peppers
4. 14 tomatoes and 14 bell peppers

Why: To solve the problem, we first need to determine the total number of parts in the ratio. The ratio 3:4 has a total of 3 + 4 = 7 parts. Since Emma is planting 28 plants, we divide the total by the number of parts: 28 / 7 = 4. Now, to find the number of tomato plants, we multiply the number of parts for tomatoes (3) by 4: 3 * 4 = 12. For bell pepper plants, we multiply the number of parts for bell peppers (4) by 4: 4 * 4 = 16. Therefore, Emma has 12 tomato plants and 16 bell pepper plants.

Carolina is organizing a community event in Austin, Texas, to promote recycling. She found that for every 3 cans she collects, she can recycle 2 of them to generate $1.50. If she has already collected 15 cans, how much money will she generate from recycling those cans?

1. $7.50 ✓
2. $10.00
3. $5.00
4. $12.50

Why: To find out how much money Carolina will generate, first, we determine how many sets of 3 cans are in the 15 cans collected. 15 cans ÷ 3 = 5 sets. Since each set generates $1.50, we multiply the number of sets by the amount generated per set: 5 * $1.50 = $7.50. Therefore, Carolina will generate $7.50 from recycling the 15 cans.

Adriana runs a small bakery in Fredericksburg. She sells cookies for $2 each and brownies for $3 each. One weekend, she sold 10 cookies and 8 brownies. If she continues to sell the same number of each item for another weekend, what will be her total earnings from selling cookies and brownies over those two weekends?

1. $88 ✓
2. $52
3. $60
4. $76

Why: To find Adriana's total earnings over the two weekends, first calculate her earnings for one weekend. For cookies, she earns 10 cookies × $2 = $20. For brownies, she earns 8 brownies × $3 = $24. So during one weekend, she earns $20 + $24 = $44. For two weekends, it would be $44 × 2 = $88. Thus, the total earnings will be $88.

Thuy is taking a field trip to Enchanted Rock with her classmates. The total cost of the trip is $180, which includes transportation and entry fees. If each student contributes $15, how many students need to participate to cover the total cost?

1. 12 ✓
2. 10
3. 15
4. 14

Why: To find out how many students need to participate, divide the total cost of the trip by the amount each student contributes. The calculation is 180 ÷ 15 = 12. Therefore, 12 students need to participate to cover the total cost.

Juan is helping his grandmother in her garden in Fredericksburg. They are planting two types of flowers: bluebonnets and sunflowers. Juan plants 3 bluebonnets for every 2 sunflowers. If he plants a total of 30 flowers, how many bluebonnets does he plant? Use the information below to find your answer.

1. 18 ✓
2. 12
3. 15
4. 9

Why: To find the number of bluebonnets Juan plants, we first establish the relationship between the bluebonnets and sunflowers. For every 3 bluebonnets, there are 2 sunflowers, which gives a total of 5 flowers in one complete set. We can set up a proportion: let x be the number of bluebonnets. Then the equation is: (3/5) * total flowers = bluebonnets. Plugging in the total flowers (30), we get (3/5) * 30 = 18. Therefore, Juan plants 18 bluebonnets.

Skylar is helping her family plant a garden in their backyard in Lufkin, Texas. They have a total space of 48 square feet for planting flowers. If each flower bed takes up 6 square feet, how many flower beds can Skylar plant in the garden?

1. 6
2. 7
3. 8 ✓
4. 9

Why: To find out how many flower beds Skylar can plant, divide the total space by the area of each flower bed. The calculation is 48 square feet ÷ 6 square feet/bed = 8 beds. Therefore, Skylar can plant 8 flower beds in the garden.