Hola i need help with this problem I got all confused with the letters
A,B,C,D and E are 5 numbers. The average of A,B,C, and E is 27. The average of B,C and D is 23. The average of B,C,D and E is 29. What is the average of these 5 numbers?
A+B+C+D=_______________=______
B+C+D=______________=______
B+C+D+E=_______________=______
From the second and third expressions, E=________________=_____
A+B+C+D+E=________________=______
The average of the 5 numbers=______________=_____
A+B+C+D=___27*4________=_108_____
B+C+D=___3*23__________=___69___
B+C+D+E=__3*29__\______=__87____
From the second and third expressions, E=________________=_____
A+B+C+D+E=________________=______
The average of the 5 numbers=______________=_____
I think the statement in the problem should have been: The average of A,B,C, and D is 27
how do u solve this?
Follow the directions on the form..
"from the second and third...
To solve this problem, start by analyzing the given information. Let's break it down step by step:
1. We are given that the average of A, B, C, and E is 27. This means that:
(A + B + C + E) / 4 = 27
2. We are also given that the average of B, C, and D is 23. This implies:
(B + C + D) / 3 = 23
3. Additionally, the average of B, C, D, and E is 29. Hence:
(B + C + D + E) / 4 = 29
Now let's solve for the missing variables using the given equations:
From equation 2, we know that B + C + D = 69 (multiply both sides by 3).
From equation 3, we have B + C + D + E = 116 (multiply both sides by 4).
By subtracting equation 2 from equation 3 (116 - 69), we find E = 47.
Now, let's substitute E = 47 in equation 1:
(A + B + C + 47) / 4 = 27
Simplifying this equation, we find A + B + C = 81 (multiply both sides by 4).
To find A + B + C + D, we add the equations from step 2 and equation 3:
B + C + D + E + B + C + D = 69 + 116
Simplifying, we get 2B + 2C + 2D + E = 185.
Since we know E = 47, we substitute the value:
2B + 2C + 2D + 47 = 185.
By subtracting 47 from both sides, we obtain:
2B + 2C + 2D = 138.
Dividing by 2, we get:
B + C + D = 69.
Now we can substitute A + B + C = 81 and B + C + D = 69 into the equation A + B + C + D + E:
A + (A + 12) = 81 + 47.
Simplifying, we find 2A + 12 = 128.
Subtracting 12 from both sides, we get 2A = 116.
Dividing by 2, we obtain:
A = 58.
Finally, to find the average of these 5 numbers, we sum them up and divide by 5:
(A + B + C + D + E) / 5 = (58 + 12 + 47 + 69 + 47) / 5 = 233 / 5 = 46.6.
Therefore, the average of these 5 numbers is 46.6.