use the five steps for problem solving. the average of two test scores is 79. if one test score is eleven less than the other, what are the two test scores?
1/2 (a + b) = 79
a - b = 11
I don't know what "five steps" you have been taught, but this is a standard algebra problem
Solve by elimination, substitution, or trial and error.
The scores will not be integers in this case.
To solve this problem using the five steps for problem solving, let's break it down step by step.
Step 1: Understand the problem.
We have two test scores, and the average of these scores is 79. One score is eleven less than the other. We need to find the two test scores.
Step 2: Devise a plan.
To solve this problem, we can set up an equation based on the information given and then solve for the unknowns.
Step 3: Carry out the plan.
Let's assign variables to represent the test scores. Let x be the score of one test, and y be the score of the other test. We know that the average of the two scores is 79, so we can write the equation:
(x + y) / 2 = 79
We're also given that one test score is eleven less than the other, which can be expressed as:
x = y - 11
Now we can substitute the value of x from the second equation into the first equation:
((y-11) + y) / 2 = 79
Simplifying this equation:
(2y - 11) / 2 = 79
Multiplying both sides of the equation by 2 to eliminate the fraction:
2y - 11 = 158
Adding 11 to both sides of the equation:
2y = 169
Dividing both sides by 2:
y = 84.5
Now we can substitute the value of y into the equation x = y - 11:
x = 84.5 - 11
x = 73.5
So the two test scores are 73.5 and 84.5.
Step 4: Look back.
We have solved for the two test scores, but let's check if they make sense. The average of 73.5 and 84.5 should indeed be 79:
(73.5 + 84.5) / 2 = 158 / 2 = 79
The calculated average matches the given information, which confirms our solution is correct.
Step 5: Communicate the solution.
The two test scores are 73.5 and 84.5.