Constraints Word Problems

Constraints are things that _______ options in problems.

• limit

• expand

Answer explanation

Constraints are factors that restrict or limit the available options in problems. Therefore, the correct choice is 'limit', as it accurately describes the role of constraints.

Tags

CCSS.HSA.CED.A.3

Which inequality represents "at least 5 people attending"?

• x > 5

• x < 5

Answer explanation

The phrase "at least 5 people attending" means that the number of attendees, represented by x, must be 5 or more. This is correctly expressed by the inequality x ≥ 5.

Tags

CCSS.6.EE.B.8

Which inequality represents "less than 4 ounces"?

• x > 4

• x < 4

Answer explanation

The phrase "less than 4 ounces" indicates that the value of x must be below 4. Therefore, the correct inequality is x < 4, which accurately represents this condition.

Tags

CCSS.6.EE.B.8

Which inequality represents "no more than 30 students"?

• x > 30

• x < 30

Answer explanation

The phrase "no more than 30 students" indicates that the number of students can be 30 or fewer. This is represented by the inequality x ≤ 30, meaning x is less than or equal to 30.

Tags

CCSS.6.EE.B.8

A student takes a test with multiple choice (m) and short answer (s) problems. Multiple choice problems are worth 2 points, short answers are worth 5 points, there are over 50 questions on the test, and no more than 200 points possible. Identify all the constraints that restrict the problem.

• m + s > 50

• 2m + 5s > 50

• m > 0

Answer explanation

The constraints include: m + s > 50 (more than 50 questions), 2m + 5s ≤ 200 (total points limit), and m > 0 (at least one multiple choice question). The other options do not correctly represent the problem's restrictions.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Emma is planning a birthday party and wants balloons and party hats. She has $20 to spend. Each balloon costs $1, and each party hat costs $2. She wants to buy at least 5 balloons. She needs to have enough items so that each of her 12 friends gets either a balloon or a hat. Emma doesn't want to buy more than 15 items in total.

Let x represent the number of balloons and y represent the number of party hats. Select all the inequalities represented by the situation.

• 1x + 2y < 20

• x > 5

Answer explanation

The total cost of balloons and hats must be less than or equal to $20, represented by 1x + 2y ≤ 20. Emma wants at least 5 balloons, so x ≥ 5. The other options do not accurately reflect the constraints.

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Emma is planning a birthday party and wants balloons and party hats. She has $20 to spend. Each balloon costs $1, and each party hat costs $2. She wants to buy at least 5 balloons. She needs to have enough items so that each of her 12 friends gets either a balloon or a hat. Emma doesn't want to buy more than 15 items in total.

Let x represent the number of balloons and y represent the number of party hats. Select all the inequalities represented by the situation.

Answer explanation

Emma needs at least 12 items for her friends, so x + y ≥ 12. She also can't buy more than 15 items total, so x + y ≤ 15. Thus, the correct inequalities are x + y ≥ 12 and x + y ≤ 15.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Emma is planning a birthday party and wants balloons and party hats. She has $20 to spend. Each balloon costs $1, and each party hat costs $2. She wants to buy at least 5 balloons. She needs to have enough items so that each of her 12 friends gets either a balloon or a hat. Emma doesn't want to buy more than 15 items in total.

Let x represent the number of balloons and y represent the number of party hats. Select all the inequalities represented by the situation.

Answer explanation

Emma needs non-negative quantities of balloons and party hats, so the inequalities x ≥ 0 and y ≥ 0 are correct. The other options are incorrect as they suggest negative quantities, which are not possible.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.C.6

CCSS.HSA.SSE.A.1

A class is planning a garden. They will plant tomatoes and carrots and have space for no more than 20 plants. They must plant at least 5 tomato plants and need to plant more carrot plants than tomato plants. Their plant budget is $30 with each tomato plant costing $2 and each carrot plant costing $1.

Let x represent the number of tomato plants and y represent the number of carrot plants. Choose all the inequalities represented by the situation.

• x + y < 20

• x + y > 20

Answer explanation

The class can plant a maximum of 20 plants, so the correct inequality is x + y ≤ 20. This ensures they do not exceed their planting space.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

A class is planning a garden. They will plant tomatoes and carrots and have space for no more than 20 plants. They must plant at least 5 tomato plants and need to plant more carrot plants than tomato plants. Their plant budget is $30 with each tomato plant costing $2 and each carrot plant costing $1.

Let x represent the number of tomato plants and y represent the number of carrot plants. Choose all the inequalities represented by the situation.

• y > x

• x > 5

Answer explanation

The inequalities represent the conditions: y > x (more carrots than tomatoes) and x ≥ 5 (at least 5 tomato plants). The other options do not accurately reflect the requirements of the garden planning.

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12