Now that you've seen the different ways context can affect the solution to a problem, try assessing some other problems you might encounter outside your classroom or online course. First, determine which of these problems are solvable, given the information provided by the problems' context. Determine whether the problem can be solved; then, click the card to see if it can be solved.
Some of the snacks for the community pool's concession stand come from a local bakery that specializes in making "square chocolate chip" cookies.
If a square chocolate chip cookie has one side that is 3 inches long and a density of .75 chocolate chips per square inch, how many chocolate chips are in each square cookie?
This problem is solvable given the context. You know the length of one side of the square, which means you know the length of every side. Therefore, you can calculate the area and then use the density formula to find out how many chocolate chips are in each cookie.
If a given location is 3 square miles and contains 30 pets, what is the density of pet cats in the location?
This problem is unsolvable given the information provided. You do not know the number (quantity) of cats in the location (only the total number of pets), so you cannot determine the density of cats in the location.
If a rectangular garden is three feet wide and contains 6 flowers, what is the density of flowers in the garden?
Not enough information is provided to allow you to calculate the density of the flowers in the garden. You would need to know the garden's area in order to complete the calculation, and you need to know the garden's length in order to calculate its area.
If a given location has a density of 15 pet dogs per square mile and the location is three square miles, how many dogs are in the location?
This question is solvable. You know the density of dogs in the location, and you know the location's area. Therefore, you can solve for density.
Cards remaining:
Problem 1
Problem 2
Some of the snacks for the community pool's concession stand come from a local bakery that specializes in making "square chocolate chip" cookies. If a square chocolate chip cookie has one side that is 3 inches long and a density of .75 chocolate chips per square inch, how many chocolate chips are in each square cookie?
Solve this problem in your notebook before clicking the button to check your answer.
There are .75 chocolate chips per square inch in a cookie, and each cookie is a 3 inch square. So the area of each cookie is 9 square inches (when we multiply length by height). Therefore, we know that .75 chocolate chips/sq. inch = chocolate chips/9 sq. inch. When we rearrange the equation, we have 9 sq. inch × .75 chocolate chips/sq. inch = 6.75 chocolate chips per cookie.
If a given neighborhood has a density of 15 dogs per square mile and the neighborhood is three square miles, how many dogs live in the neighborhood?
In your notebook, calculate the number of dogs in this neighborhood. Then, click the button to check your answer.
Because the density is already given as the number of dogs divided by the area of the location, you simply multiply the density by the area in order to figure out the number of dogs. For this problem, that's 15 dogs per square mile multiplied by 3 square miles, or 45 dogs total.
