TEKS 6.5A Worksheets — Grade 6 Represent mathematical and real-world problems involving ratios

Tatiana wants to save money to buy a bicycle that costs $240. She saves $30 each week. After how many weeks will she have enough money to buy the bicycle?

1. 8 ✓
2. 6
3. 10
4. 12

Why: To find out how many weeks it will take Tatiana to save enough money, divide the total cost of the bicycle by the amount she saves each week. So, $240 ÷ $30 = 8 weeks. Therefore, Tatiana needs 8 weeks to save enough money to buy the bicycle.

Mason is creating a model of a Texas A&M football field for a school project. The actual field is 100 yards long and 53 1/3 yards wide. Mason wants to make a scale model that is 1/4 the size of the actual field. What will be the dimensions of Mason's model in yards?

1. 25 yards long and 13 1/3 yards wide ✓
2. 20 yards long and 10 1/4 yards wide
3. 30 yards long and 15 yards wide
4. 22 1/2 yards long and 11 1/4 yards wide

Why: To find the dimensions of Mason's model, we need to multiply both dimensions of the actual football field by the scale factor of 1/4. The length of the field is 100 yards, so 100 * 1/4 = 25 yards. The width of the field is 53 1/3 yards, which is the same as 160/3 yards (since 53 1/3 = 160/3). Now, we multiply that by 1/4: (160/3) * (1/4) = 160/12 = 40/3 = 13 1/3 yards. Therefore, Mason's model will be 25 yards long and 13 1/3 yards wide.

Amelia is organizing a lemonade stand at the State Fair of Texas. She plans to make 5 gallons of lemonade. The recipe requires 2/3 of a gallon of lemon juice for every gallon of lemonade. How many gallons of lemon juice will Amelia need for her 5 gallons of lemonade?

1. 3 1/3 ✓
2. 2 1/2
3. 4
4. 3

Why: To find out how much lemon juice Amelia needs, multiply the number of gallons of lemonade by the amount of lemon juice per gallon. The calculation is 5 * (2/3) = 10/3. When you convert 10/3 to a mixed number, it equals 3 1/3 gallons. Therefore, Amelia will need 3 1/3 gallons of lemon juice.

Theodore is helping his family set up a booth at the Texas State Fair to sell homemade salsa. They made 18 jars of mild salsa and 24 jars of spicy salsa. Theodore wants to create a ratio of mild salsa to the total number of jars of salsa made. What is this ratio expressed in simplest form?

1. 3/7 ✓
2. 3/4
3. 2/3
4. 5/3

Why: To find the ratio of mild salsa to the total number of jars, first calculate the total number of jars: 18 + 24 = 42. Then, the ratio of mild salsa (18) to the total (42) is 18/42. To simplify this, divide both the numerator and denominator by 6: 18 ÷ 6 = 3 and 42 ÷ 6 = 7. Thus, the simplest form of the ratio is 3/7.

Diego is preparing for a science fair project about the wildlife in Palo Duro Canyon. He wants to create a scaled map of the canyon. If the actual length of the canyon is 120 miles and he wants his map to have a scale of 1 mile represented as 1/4 inch, how long will the canyon be on Diego's map in inches?

1. 30 ✓
2. 20
3. 15
4. 40

Why: To find the length of the canyon on the map, we first convert the actual length of the canyon from miles to inches using the scale. Since 1 mile is represented as 1/4 inch, we need to calculate the total inches for 120 miles. So, we multiply 120 miles by 1/4 inch/mile: 120 * (1/4) = 30 inches. Therefore, the length of the canyon on Diego's map will be 30 inches.

Hannah is organizing a bake sale for her school's fundraiser. She plans to make chocolate chip cookies and brownies. She wants the ratio of chocolate chip cookies to brownies to be 3 to 2. If she bakes a total of 30 treats, how many chocolate chip cookies will she make?

1. 18 ✓
2. 15
3. 12
4. 10

Why: To find the number of chocolate chip cookies, we first understand the total parts in the ratio 3 to 2, which is 3 + 2 = 5 parts. Each part represents 30 treats divided by 5 parts, which is 6 treats per part. Since the ratio of cookies is 3 parts, we multiply 6 treats by 3, resulting in 18 chocolate chip cookies.

Imani is baking cookies for a school bake sale. She has a recipe that makes 24 cookies using 3 cups of flour. If Imani wants to make 48 cookies for the bake sale, how many cups of flour will she need?

1. 6 cups ✓
2. 4 cups
3. 8 cups
4. 5 cups

Why: To find out how many cups of flour Imani needs for 48 cookies, we can see that 48 is double the amount of 24. Since the recipe uses 3 cups of flour for 24 cookies, Imani will need 3 * 2 = 6 cups of flour for 48 cookies.

Oliver is helping his family prepare for the Texas State Fair. They are making cotton candy, which requires 3 cups of sugar for every 5 servings. If they want to make 30 servings, how many cups of sugar do they need in total?

1. 18 ✓
2. 15
3. 12
4. 20

Why: To find out how many cups of sugar are needed for 30 servings, first determine the ratio of sugar to servings. For 5 servings, 3 cups of sugar are needed. Therefore, for 30 servings, you can set up the proportion: (3 cups / 5 servings) = (x cups / 30 servings). Cross-multiplying gives us: 5x = 90. Solving for x, we get x = 90 / 5, which equals 18. So, Oliver needs 18 cups of sugar in total.