Unit 2 Study Guide

Mathematical Equivalence

OFF

1. A car rental agency charges $75 per day, which includes 100 miles. For each mile over 100 miles, there is an additional cost of $0.35 per mile. 

2. Write an equation relating 

3. x, the number of miles driven, if the total cost for a one-day rental was $131.

• 75x+0.35(x-100)=131

• 75+0.35(x-100)=131

• 75+0.35x=131

1. The surface area, S , of a cone is calculated using the formula S =𝝅rl + 𝝅r². 

2. Which equation is equivalent to the formula solved for l, the slant height of the cone?

1. Tickets to the zoo cost $15 for adults and $11 for children. The school has a budget of $1500 for the field trip. An equation representing the budget for the trip is 15x+11y=1500.

2. With a budget of $1500, determine if 120 students and 20 adults can go to the zoo.

• yes

• no

1. Tickets to the zoo cost $15 for adults and $11 for children. The school has a budget of $1500 for the field trip. An equation representing the budget for the trip is 15x+11y=1500.

2. If there are 120 students who need tickets, what is the maximum number of adults who can go to the zoo while staying within the school budget?

Mathematical Equivalence

ON

• a

• b

• c

• d

1. The gardening club at school is growing vegetables. The club has 250 square feet of planting beds. Zucchini plants require five square feet of growing space, and bell pepper plants require six square feet of growing space. The students want to plant some of each type of plant and have at least 45 plants. 

Select the equation or inequality that could describe a part of this situation. Let z represent the number of zucchini plants and p represent the number of bell pepper plants.

​

• z>0

• 1. p<0

• 1. z+p=250

• 1. 5z+6p>250

1. The gardening club at school is growing vegetables. The club has 250 square feet of planting beds. Zucchini plants require five square feet of growing space, and bell pepper plants require six square feet of growing space. The students want to plant some of each type of plant and have at least 45 plants. 

Select the equation or inequality that could describe a part of this situation. Let z represent the number of zucchini plants and p represent the number of bell pepper plants.

​

• z<0

• 1. p<0

• 1. z+p=250

1. A local artist is selling their art pieces at an art fair. It costs $150 to rent a booth at the fair. The cost of materials for each piece of art is $5. The artist is selling each piece for $30 each.

2. The inequality 30x>150+5x represents the situation in which the artist makes a profit.

   1. Will the artist make a profit if he sells 5 art pieces?

• yes

• no