QIf the average of 3 numbers is 87, and the first number is 4 times the second number and 5 times the third number, what is the difference between the first and third numbers?
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Explanation
Let's call the first number A, the second number B, and the third number C. We know that the first number is 4 times the second number and 5 times the third number, so we can represent these relationships with the equations:
A = 4B
A = 5C
We also know that the average of the three numbers is 87, so we can represent this with the equation:
(A + B + C)/3 = 87
We can solve this system of equations using substitution or elimination.
Using substitution, we can solve for B in the first equation and substitute it into the second equation:
B = A/4
5C = A
C = A/5
Substituting these values for B and C back into the first equation, we get:
(A + A/4 + A/5)/3 = 87
5A + A + 4A/5 = 261
9A = 1020
A = 180
We can check our solution by substituting this value for A back into the other two equations to make sure they both hold true.
A = 4B => 180 = 4B => B = 45
A = 5C => 180 = 5C => C = 36
Since both equations hold true, we have found a valid solution.
To find the difference between the first and third numbers, we can simply subtract the third number from the first number:
A - C = 180 - 36 = 144
So the difference between the first and third numbers is 144
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