6x+Q=Px+15 what values of P and Q result in an equation with exactly one solution?
1 answer:
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Answer:
The third number (c) is 54.
The other ones are 70 and 56.
Step-by-step explanation:
We have 3 numbers, let's call them a, b and c.
We know that the sum of the three numbers is 180, thus:
We also know that the first number is 10 more than the mean of the three numbers <em>(Note: the mean is the sum of the numbers divided by the number of numbers).</em> Thus:
Finally the second number is 4 less than the mean:
Now we have our set of equations and we can proceed to solve them:
Solving for a in our first equation we have: and substituting this in our second equation we have:
Now taking this last result into our first equation we have:
Now we are going to solve for b in our second equation and substitute this in our third equation:
But we know that a =70, so we can substitute it in our last line:
Now we just need to find b and we can use our first original equation to do this: