Lesson 4 Equations and their Solutions

Lesson 4 Equations and their Solutions

Multiple Select

An artist is selling children's crafts. Necklaces cost $2.25 each, and bracelets cost $1.50 per each.

Select all the combinations of necklaces and bracelets that the artist could sell for exactly $12.00.

• 5 necklaces and 1 bracelet

• 2 necklaces and 5 bracelets

• 3 necklaces and 3 bracelet

• 4 necklaces and 2 bracelets

• No necklaces and 8 bracelets

Multiple Select

Diego is collecting dimes and nickels in a jar. He has collected $22.25 so far. The relationship between the numbers of dimes and nickels, and the amount of money in dollars is represented by the equation 0.10d+0.05n=22.25.

Select all the values (d,n) that could be solutions to the equation.

• (0,445)

• (0.50,435)

• (233,21)

• (118,209)

• (172,101)

Multiple Select

Volunteer drivers are needed to bring 80 students to the championship baseball game. Drivers either have cars, which can seat 4 students, or vans, which can seat 6 students. The equation 4c+6v=80 describes the relationship between the number of cars, c, and number of vans, v, that can transport exactly 80 students.

Select all statements that are true about the situation.

• If 12 cars go, then 2 vans are needed.

• c=14 and v=4 are a pair of solutions to the equation.

• If 6 cars go and 11 vans go, there will be extra space.

• 10 cars and 8 vans isn’t enough to transport all the students.

• If 20 cars go, no vans are needed.

Multiple Choice

Kiran’s family is having people over to watch a football game. They plan to serve sparkling water and pretzels. They are preparing 12 ounces of sparkling water and 3 ounces of pretzels per person. Including Kiran’s family, there will be 10 people at the gathering.

A bottle of sparkling water contains 22 ounces and costs $1.50. A package of pretzels contains 16 ounces and costs $2.99. Let n represent number of people watching the football game, s represent the ounces of sparkling water, p represent the ounces of pretzels, and b represent Kiran’s budget in dollars. Which equation best represents Kiran’s budget?

• $12s+3p=b$
  

• $12\cdot10+3\cdot10=b$

• $1.50s+2.99p=b$

• $1.506+2.992=b$

Open Ended

The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed, S, be measured in feet per second.

Write an equation to represent the relationship between the three quantities (speed, distance, and time).

Multiple Choice

A donut shop made 12 dozen donuts to give to a school’s math club.

Which expression represents how many donuts each student would get if the donuts were equally distributed and there were x students in math club?

• $\frac{x}{12}$

• $12\cdot\frac{x}{12}$

• $\left(12\cdot12\right)x$

• $12\cdot12$