Use the five steps for problem solving to answer the following question. Please show all of your work.
The average of two quiz scores is 81. If one quiz score is six more than the other quiz score, what are the two quiz scores?
Denise or Franklin -- please do not change screen names on this forum
What are the five steps for problem solving?
familiarize, translate, carry out, check and state
Thank you.
I showed you how to do the first three steps in your last post.
Now it's your turn. I'll be glad to check your answer.
ok give me a second or longer, thanks
n + n + n + 6 = 81 * 2
3n + 6 = 162 - 6
3n = 156
n=156/2
n=78
this isn't right what am I doing wrong?
To start, you have 3n -- but you only have 2 test scores.
Your answer of 78 is correct for the first score. Add 6 to it for the other score.
78 + 84 = 162
162/2 = 81
Step 1: Understand the problem
We are given that the average of two quiz scores is 81 and that one quiz score is six more than the other quiz score. We need to find the two quiz scores.
Step 2: Devise a plan
To find the two quiz scores, we can set up a system of equations and solve them simultaneously. Let's use variables to represent the quiz scores.
Step 3: Carry out the plan
Let's assume that one quiz score is x, and the other quiz score is y. We know that the average of the two scores is 81, so we can write the equation:
(x + y) / 2 = 81
We also know that one score is six more than the other, which gives us the equation:
x = y + 6
Now we can substitute the value of x from the second equation into the first equation:
((y + 6) + y) / 2 = 81
(2y + 6) / 2 = 81
2y + 6 = 162
Simplify the equation:
2y = 162 - 6
2y = 156
Divide both sides by 2:
y = 78
Now substitute the value of y back into the equation x = y + 6:
x = 78 + 6
x = 84
So the two quiz scores are 78 and 84.
Step 4: Review the solution
We found that the two quiz scores are 78 and 84, and we can double-check our answer by calculating their average: (78 + 84) / 2 = 162 / 2 = 81.
Step 5: Reflect on the solution
We successfully used the steps for problem-solving to find the two quiz scores, which are 78 and 84.