6.08 Linear Inequalities for Home and Jobs

A homeowner wants to paint a wall and has a budget of $50 for paint. Each gallon of paint costs $15, and each brush costs $5. Write an inequality to represent the maximum number of gallons of paint (x) and brushes (y) the homeowner can buy.

Answer explanation

The total cost for x gallons of paint at $15 each and y brushes at $5 each must not exceed the budget of $50. This is represented by the inequality 15x + 5y ≤ 50, making the correct choice the first option.

A person is building a bookshelf and needs to cut wooden planks. Each plank costs $8, and each nail costs $0.50. The person has $64. Write an inequality to represent the maximum number of planks (x) and nails (y) the person can purchase.

Answer explanation

The total cost for planks and nails must not exceed $64. Each plank costs $8 (8x) and each nail costs $0.50 (0.5y). Therefore, the correct inequality is 8x + 0.5y ≤ 64, representing the maximum budget.

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn.

Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

Answer explanation

To find the minimum hours Joan needs to babysit, let x be the hours. She earns $5 per hour, plus $10 from mowing. The inequality 5x + 10 ≥ 100 represents her total earnings needing to be at least $100.

Tags

CCSS.7.EE.B.4B

A DIY enthusiast is planning to build a garden box. The wood costs $5 per foot, and nails cost $0.25 each. The total budget for wood and nails is $100. Write an inequality to represent the maximum length of wood (x) and number of nails (y) that can be purchased.

• 5x + 0.25y > 100

• 5x + 0.25y < 100

• x + y > 100

• 5x + y < 100

Answer explanation

The cost of wood is $5 per foot (x) and nails are $0.25 each (y). The total budget is $100, so the correct inequality is 5x + 0.25y < 100, representing the maximum length of wood and number of nails that can be purchased.

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 plus $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450

• 0.85x + 375 < 450

• 0.85 + 375x > 450

• 0.85 + 375x < 450

Answer explanation

To find the number of miles, x, the driver needs to drive, we set up the inequality: rental fee ($375) plus $0.85 per mile (0.85x) must be greater than $450. Thus, the correct inequality is 0.85x + 375 > 450.

Tags

CCSS.7.EE.B.4B

A homeowner is installing tiles in a room. Each tile costs $3, and each bag of grout costs $10. The homeowner has $90. Write an inequality to represent the maximum number of tiles (x) and bags of grout (y) that can be purchased.

Answer explanation

The total cost for tiles and grout must not exceed $90. Each tile costs $3 (3x) and each bag of grout costs $10 (10y). Therefore, the correct inequality is 3x + 10y ≤ 90, representing the maximum budget.

A baker is buying ingredients for a large order. Each bag of flour costs $10, and each dozen eggs costs $3. The baker has $90. Write an inequality to represent the maximum number of bags of flour (x) and dozens of eggs (y) that can be purchased.

Answer explanation

The total cost for x bags of flour and y dozens of eggs must not exceed $90. Each bag of flour costs $10 and each dozen eggs costs $3, leading to the inequality 10x + 3y ≤ 90, which represents the maximum purchase.

A gardener is buying supplies for a landscaping project. Each bag of soil costs $12, and each plant costs $5. The gardener has a budget of $120. Write an inequality to represent the maximum number of bags of soil (x) and plants (y) that can be purchased.

Answer explanation

The total cost for x bags of soil at $12 each and y plants at $5 each must not exceed the budget of $120. This is represented by the inequality 12x + 5y ≤ 120, making it the correct choice.

A gardener is buying flowers for a spring garden. Each flat of pansies contains 16 plants and each pot of daffodils has 3 plants. The gardener wants at least 200 plants in the flower bed. Write an inequality to represent the maximum number of flat of plants that need to be purchased to meet the goal.

Answer explanation

The inequality must account for both types of plants. Let x be the number of flats of pansies and y the number of pots of daffodils. Each flat has 16 plants and each pot has 3, so the correct inequality is 16x + 3y ≥ 200.

A chef is preparing a large meal and needs to buy ingredients. Each pound of chicken costs $7, and each pound of vegetables costs $2. The chef has a budget of $70. Write an inequality to represent the maximum number of pounds of chicken (x) and vegetables (y) that can be purchased.

Answer explanation

The cost of chicken is $7 per pound (x) and vegetables $2 per pound (y). The total cost must not exceed $70, leading to the inequality 7x + 2y ≤ 70, which represents the budget constraint.