Tutor profile: Nora M.
D is between C and E. If CE = 6x, CD = 4x + 8, and DE = 27, then find CE.
Sometimes the easiest thing to do in geometry is draw a picture. ______________________ C D E As you can see, the problem says that D is somewhere between C & E but does not say that is it in the middle so you do not want to draw it there to add to the confusion. Next, label the other information that you are given on your picture. 6x ______________________ C D E 4x + 8 27 Now, using the Segment Addition Postulate create your equation from the information given. 4x + 8 + 27 = 6x 4x + 35 = 6x (Combine Like Terms (CLT)) Subtract 4x from each side 4x - 4x + 35 = 6x - 4x 35 = 4x Divide by 4 on each side 35/4 = 4x/4 17.5 = x But this is NOT our final answer! The question is asking you to find CE, so you will have to plug in your found x into CE. CE = 6x = 6(17.5) = 105 Therefore, your answer is CE = 105
331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were on each bus?
The first thing we need to do is establish a variable for whatever it is the question is asking you to find. In this case, we will have x = number of students (on each bus). The next thing we need to do is find the total number of students that went on the trip. This will be on one side of the equal sign by itself. (331 students) Converting the sentences into an equation we can say that: 6x + 7 = 331 (remember, x represents the number of students on each bus) subtract 7 from each side of the equal sign in order to get 6x by itself 6x +7 - 7= 331 - 7 6x = 324 divide each side by 6 to solve for x 6x/6 = 324/6 x = 54 Therefore, there are 54 students on each bus.
A gym offers two options for membership plans. Option A includes an initiation fee of $121 and costs $1 per day. Option B has no initiation fee but costs $12 per day. After how many days will the total cost of each gym membership plans be the same?
First, you need to establish a variable to represent exactly what you are trying to find so we're going to say that x = the number of days. At the beginning of the question, you are given specific information for gym Option A that will be converted into an expression using our variable, x. Option A = 121 + 1x There is information given for gym Option B that will be converted as well. Option B = 12x The last sentence tells you that each of the gym options will be the same cost. This means that Option A and Option B will be equal to each other so creating an equation we get: Option A = Option B 121 + 1x = 12x (substitute our expressions into the established equation) 121 = 11x (subtract the smallest variable to the other side) 11 = x (divide by the number with the variable) So this means that after 11 days the gym membership costs will be the same.
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