Solving Two-Variable Inequalities

A rental car company charges $74.90 per day to rent a car and $0.13 for every mile driven. Tyee wants to rent a car, knowing that he plans to drive 175 miles and has at most $210 to spend.

Determine x, the number of days Tyee can afford to rent while staying within his budget.

• Tyee can afford to rent the car for 2 days.
• Tyee can afford to rent the car for 1 day.
• Tyee can afford to rent the car for 3 days.
• Tyee can afford to rent the car for 5 days.

A shipping container can hold a maximum weight of 23,500 kilograms. So far, 12,100 kilograms have already been loaded into the container. Each crate being added weighs 40 kilograms. Write an equation in slope-intercept form to represent the total weight y of the container based on the number of crates x added.

Then, determine the maximum number of crates that can be added without exceeding the weight limit.

• 150
• 285
• 200
• 320

A group of friends wants to go to the amusement park. They have no more than $250 to spend on parking and admission. Parking is $12.25, and tickets cost $22.25 per person, including tax. What is the maximum number of people who can go to the amusement park?

• 5
• 15
• 20
• 10

Jonathan has a points card for a movie theater. He receives 25 rewards points just for signing up.

He earns 13.5 points for each visit to the movie theater. He needs at least 135 points for a free movie ticket.

What is the least number of visits he needs to make in order to earn a free movie ticket?

• 5 visits

• 12 visits

• 7 visits

• 9 visits

Carter and his children went into a restaurant and will buy hotdogs and drinks. Each hotdog costs $3.50 and each drink costs $1.50. Carter has a total of $45 to spend on hotdogs and drinks.

Determine the possible values for the number of hotdogs purchased, h, and the number of drinks purchased, d so that he doesn't overspend.

• 15 hotdogs and 10 drinks

• 5 hotdogs and 30 drinks

• 20 hotdogs and 5 drinks

• 10 hotdogs and 2 drinks

Aaliyah and her children went into a bakery and will buy donuts and brownies. She must buy a minimum of 11 donuts and brownies all together.

Determine the number of donuts purchased, d, and the number of brownies purchased, b.

• 7 donuts and 5 brownies

• 6 donuts and 5 brownies

• 7 donuts and 2 brownies

• 2 donuts and 3 brownies

Ximena and her children went into a restaurant and will buy hamburgers and tacos. Each hamburger costs $5.50 and each taco costs $4. Ximena has a total of $35 to spend on hamburgers and tacos.

Determine the maximum number of hamburgers purchased, h, and the number of tacos purchased, t that can be purchased without going over budget.

• 4 hamburgers and 3 tacos

• 6 hamburgers and 0 tacos

• 3 hamburgers and 5 tacos

• 5 hamburgers and 2 tacos

An event planner, is ordering centerpieces and garlands for a holiday party. Each garland, x, costs $46 and each centerpiece, y, costs $12. The planner has been given a total floral budget of no more than $970.

Which of the following is a possible combination?

• 5 centerpieces and 25 garlands
• 10 centerpieces and 20 garlands

• 8 centerpieces and 18 garlands
• 12 centerpieces and 20 garlands

Brad is baking a multi-tiered cake for a friend's wedding. An eight-inch cake tier will feed 23 guests and a twelve-inch tier will feed 37 guests. In total, these tiers must feed at least 334 guests, the number attending the wedding.

If he has 3 eight-inch cake tiers and 4 twelve-inch cake tiers, will have have enough to feed his guests at the wedding?

• Yes, but he will have a lot of leftovers.

• No, he will not have enough cake.

• Yes, there is just enough cake.