Hi, I have two questions here I need help with, thank you in advance.
1. Peggy scored 68 on her first three tests of the term. What would she have to score on the fourth test to have an average of 70 on the fourth test?
2. If you were to place the digits 1,2,4,8,9, one per box, to find the largest possible quotient, what would the quotient be?
Diagram for above ^^^^^^
box box box / box box
68*3 + x = 70*4
you want large on top and small on bottom, so
984/12
1. To find out what Peggy would need to score on her fourth test to have an average of 70, we can use the formula for average:
Average = (Sum of Scores) / (Number of Scores)
In this case, Peggy has taken three tests and wants to have an average of 70 after the fourth test. The sum of her scores after the third test is 68, and the number of scores is 3.
So the equation becomes:
70 = (68 + Fourth Test Score) / 4
To solve for the fourth test score, we can multiply both sides of the equation by 4:
280 = 68 + Fourth Test Score
Next, subtract 68 from both sides of the equation:
Fourth Test Score = 280 - 68
Simplifying, we find that Peggy would need to score 212 on her fourth test to have an average of 70 for all four tests.
2. To find the largest possible quotient using the digits 1, 2, 4, 8, and 9, we can consider the placement of the digits in the numerator and denominator.
To create the largest quotient, we need to place the largest digit in the numerator's leftmost box (position of highest place value) and the smallest digit in the denominator's rightmost box.
Using the given digits, the largest quotient can be formed as follows:
9
-------
1
Therefore, the largest possible quotient using the digits 1, 2, 4, 8, and 9 is 9/1, which equals 9.
Hello! I'd be happy to help you with your questions. Let's start with the first one:
1. To find out what Peggy would have to score on the fourth test to have an average of 70, we need to consider the total score and the number of tests she has taken so far.
In this case, Peggy scored 68 on her first three tests. To find her average, we divide the total score by the number of tests:
Average = Total Score / Number of Tests
So far, Peggy has taken three tests, and her average needs to be 70. Let's use the variable "x" to represent her score on the fourth test.
To find out what Peggy would need to score on the fourth test, we set up the equation:
(68 + 68 + 68 + x) / 4 = 70
We added up the scores of the first three tests (68 + 68 + 68) and divided by the total number of tests (4). We set this equal to 70, which is the desired average.
Now, we need to solve for the variable "x" to find Peggy's required score on the fourth test.
To isolate "x," we can start by multiplying both sides of the equation by 4:
68 + 68 + 68 + x = 70 * 4
Now, simplify the equation:
204 + x = 280
Next, subtract 204 from both sides to isolate "x":
x = 280 - 204
Simplifying further, we get:
x = 76
Therefore, Peggy would need to score 76 on the fourth test to have an average of 70.
Let's move on to your second question:
2. To find the largest possible quotient using the digits 1, 2, 4, 8, and 9, one per box, let's create the visual representation:
4 9 8
-------
1 2
In this division problem, the dividend (the number being divided) consists of the digits 498 written from left to right. The divisor (the number doing the dividing) consists of the digits 12 written from left to right.
To find the largest possible quotient, we want the highest value for the dividend and the lowest value for the divisor. So, we place the highest digit, 9, in the first box of the dividend, and the lowest digit, 1, in the first box of the divisor.
Now, let's solve the division problem:
49
-----
12)498
To find the quotient, we divide 498 by 12:
The largest whole number quotient you can get is 41, with a remainder of 6. So the quotient is 41.
I hope this helps! Let me know if there's anything else I can assist you with.