SOLUTION: The average (arithmetic mean) of a and b is 10, whereas the average of b and 10 is c/2. What is the average of a and c?
Algebra.Com
Question 258316: The average (arithmetic mean) of a and b is 10, whereas the average of b and 10 is c/2. What is the average of a and c?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(a+b)/2 = 10 (first equation)
(b+10)/2 = (c/2) (second equation)
first equation states that the average of a and b is 10.
second equation states that the average of b and 10 is c/2
question is what is the average of a and c.
take the second equation and solve for b.
second equation is:
(b+10)/2 = c/2
multiply both sides of this equation by 2 to get:
b + 10 = c
subtract 10 from both sides of this equation to get:
b = c - 10
substitute for b in the first equation.
first equation is:
(a+b)/2 = 10
multiply both sides of this equation by 2 to get:
a + b = 20
subsstitute (c-10) for b to get:
a + c - 10 = 20
add 10 to both sides of this equation to get:
a + c = 30
divide both sides of this equation by 2 to get:
(a+c)/2 = 15
average of (a+c) is equal to 15.
RELATED QUESTIONS
The average (arithmetic mean) of a , a+1 , and a+2 is c , and the average of b , b+1 ,... (answered by tommyt3rd)
The average (arithmetic mean) of r, s, x and y is 8, and the average of x and y is 4.... (answered by MathLover1)
The average (arithmetic mean) of 80, 83, 89, and x is the same as the average of 80,... (answered by ankor@dixie-net.com)
If the average (arithmetic mean) of seven numbers is -8 and the average of five of the... (answered by Fombitz)
If the average (arithmetic mean) of eight numbers is 20 and the average of five of these... (answered by stanbon)
If the average (arithmetic mean) of six numbers is 28 and the average of two of these... (answered by KMST)
if 5a+5b=45, what is the average(arithmetic mean) of a and... (answered by Fombitz,checkley77)
The average(arithmetic mean) of nine numbers is 9. When a tenth number is added the... (answered by edjones)
If a+b=7(c+d), what would be the average (arithmetic mean) of a, b, c and... (answered by Fombitz)