The average of 5 numbers is 28. What would the 6th number have to be to bring the average up to 30?
Anne’s average in math is 92. She wants to raise her average to 93 so she will make an A. she is taking a test on Friday. What score will she have to make on the test to raise her average to 93?
Do you have sufficient information to solve this problem?
If yes, what is the score? If no, supply any data you need to answer the questions.
if the average of 5 numbers is 28, the total of the 5 numbers is 5(28) or 140
so (140 + x)/6 = 30
times 6
140 + x = 180
x = 180-140
x = 40
notice in the 2nd, you don't have enough information.
You have to know how many tests gave Anne her average of 92
To find the sixth number in the given set of 5 numbers, we can use the concept of averages.
Let’s assume the sum of the first 5 numbers is N. Since the average of these numbers is given as 28, we can calculate N as follows:
N = Average × Number of Numbers
N = 28 × 5
N = 140
Now, to find the sixth number, let's assume it as X. We need to find the value of X that will make the average of all 6 numbers equal to 30.
The sum of all 6 numbers will be N + X.
The average of all 6 numbers will be (N + X) ÷ 6.
To make the average equal to 30, we can set up an equation:
(N + X) ÷ 6 = 30
Substitute N = 140 into the equation:
(140 + X) ÷ 6 = 30
Multiply both sides of the equation by 6 to isolate the variable:
140 + X = 180
Solve for X:
X = 180 - 140
X = 40
Therefore, the sixth number should be 40 to bring the average up to 30.
For the second question about Anne's math average, we are given her current average as 92 and her goal average as 93. We need to determine the score she needs on her test in order to raise her average.
Let's assume Anne has already taken n tests with an average of 92. The total sum of her scores for these n tests would be 92n.
Now, Anne wants to raise her average to 93 by taking one more test. Let's assume her score on the test is X.
To calculate the new average, we add Anne's total scores on the n tests and her score on the new test, then divide by the total number of tests (n + 1):
(92n + X) ÷ (n + 1) = 93
Since we are given that she wants to make an A, we assume X is an integer.
Simplifying the equation:
92n + X = 93(n + 1)
92n + X = 93n + 93
Subtracting 92n from both sides:
X = 93n + 93 - 92n
X = n + 93
From the equation, we can conclude that X (Anne's score on the test) must be one more than the number of tests she has taken so far in order to raise her average to 93.
Therefore, Anne needs to score n + 1 on the test to raise her average to 93.