A student missed 71 problems on a biology test and received a grade of 22%. If all the problems were of equal value, how many problems were on the test? Follow the problem-solving process and round your answer to the nearest integer.
Well, if the student missed 71 problems and received a grade of 22%, then we can figure out how many problems were on the test by doing some math.
First, let's find the total number of problems the student attempted. We know that they received a grade of 22%, which means they got 22% of the problems correct. So, we can set up an equation like this:
71 = 0.22x
To solve for x, the total number of problems on the test, we need to divide both sides of the equation by 0.22.
Let me grab my calculator...
*beep boop beep*
Alright! After crunching the numbers, it looks like the total number of problems on the test is approximately 322.
So, to answer your question, there were around 322 problems on the biology test. Hope that puts a smile on your face!
To solve this problem, we can set up a proportion to find the total number of problems on the test.
Let "x" represent the total number of problems on the test.
The student missed 71 problems, so the number of problems answered correctly would be x - 71.
The student received a grade of 22%, which means the number of problems answered correctly is 22% of the total number of problems. We can write this as:
(x - 71) = 0.22x.
Now, let's solve this proportion:
x - 71 = 0.22x
x - 0.22x = 71
0.78x = 71
x = 71 / 0.78
x ≈ 91.
Rounding this to the nearest integer, we can conclude that there were approximately 91 problems on the test.
To find the total number of problems on the biology test, we can use the information given about the number of missed problems and the grade received.
Let's start with the grade received of 22%. This means that the student got 22% of the total possible points.
We can represent the number of problems missed using an unknown variable, let's say "x".
Since the grade is based on the number missed, we can set up an equation:
(100% - 22%) = (x missed problems / total number of problems)
78% = (x / total number of problems)
Now, we can solve for the total number of problems by cross-multiplying:
78% * total number of problems = x missed problems
To remove the percentage, we can convert it to a decimal by dividing it by 100:
0.78 * total number of problems = x missed problems
Now, we have an equation that relates the number of missed problems (x) to the total number of problems.
We know that the student missed 71 problems, so we can substitute that value into the equation:
0.78 * total number of problems = 71 missed problems
To solve for the total number of problems, we divide both sides of the equation by 0.78:
total number of problems = 71 missed problems / 0.78
Calculating this gives us:
total number of problems ≈ 91.03
Since we have to round the answer to the nearest integer, the total number of problems on the test is approximately 91.
the student got 22% correct ... so, 78% wrong
total problems = 71 / .78