Tutor profile: Robin M.
In Tech Ed class, students create tables of different shapes that all have the same area. Student A built a circular table that is 6 feet wide. If Student B built a rectangular table that is also 6 feet wide, find the length of the rectangular table. (Use 3.14 for pi).
To solve this problem, I first read through and pick out key information. From reading the problem I know that the circle and rectangle both have the same area. I then think about the formulas for finding the area of each shape and determine what information I have. For a circle, the formula for finding area is pi * radius * radius and the formula for calculating the area of a rectangle is length * width. I am given the width of the circular table, which is the diameter. However, I know that the radius of a circle is half the length of the diameter, so I can calculate the radius to be 6/2 or 3 feet. I only have one dimension of the rectangular table, so I will need to find the area of the circle and then work backwards to find the length of the rectangle. The area of the circular table can be calculated by multiplying 3.14 * 3 * 3 = 28.26 square feet. Since the problem tells me that the two have the same area and I have 1 unknown, I can create and solve an equation to find the missing dimension of the rectangle. The equation I can create is 28.26 = 6x. Now I can use inverse operations to solve the equation for the missing dimension. By dividing both sides of the equation by 6, 28.26 ÷ 6 = 4.71 feet long. The length of the rectangular table is 4.71 feet.
Betty bought a 10 pound bag of jelly beans for $45. How can Betty use this information to calculate the price for only 1 pound? How can Betty use this information to calculate how much 4 pounds would cost? Can Betty calculate the cost of x pounds?
Since Betty knows 10 pounds cost $45 and she wants to find the cost for a pound, she can calculate the unit rate of the jelly beans. To calculate the unit rate, Betty can divide 45 total dollars by 10 total pounds which is $4.50 per pound. Since Betty knows the cost for 1 pound, she can multiply this by any number of pounds. So to calculate the cost of 4 pounds Betty can multiply 4 pounds by $4.50 per pound or $18.00. I know this answer makes sense because it should be less than $45 which is the cost for 10 pounds.
On the weekend, Charles played 4 more than twice the number of games Steve did. Together, the two played 14 total games. How many games did Steve play?
To begin solving this question, I would first look for key information that will help me in finding the solution. I know that I have an unknown because the question asks for the number of games one of the participants played. Some key words I can decipher are more than indicates the problem will include addition, twice indicates I will be multiplying something by 2 and 14 total games means my expression will be set equal to 14. Since the number of games Steve played is the unknown in the problem, I will use a variable of x to represent the number of games Steve played. Reading through the problem I can create an equation of 4 + (4 more than) 2x (twice the number of games Steve played) = 14 (the total number of games). So the final equation is 4 + 2x = 14. From there I can use inverse operations to solve the equation for the unknown variable. Begin solving by subtracting the constant to the other side, since the inverse of positive 4 is negative 4 and I need to create a sum of 0. Since equations are like a seesaw, I must keep the equation balanced and subtract 4 on the other side of the equal sign as well, leaving an equation of 2x = 10. Finally, two and the variable x are being multiplied together so to isolate the variable use the inverse of multiplication which is division and divide 10 by 2. 10 divided by 2 is 5 leaving a solution of x = 5. Steve played 5 games.
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