SOLUTION: The sum of two numbers is 40. If twice the larger number is divided by the smaller, the quotient is 3 and the reminder is 10. Find the number. I NEED HELP. PLEASE!!!! The answer i
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Question 121888This question is from textbook algebra: structure and Method: book 1
: The sum of two numbers is 40. If twice the larger number is divided by the smaller, the quotient is 3 and the reminder is 10. Find the number. I NEED HELP. PLEASE!!!! The answer is 26 or 14, but I do not know how to get there.
This question is from textbook algebra: structure and Method: book 1
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let one of the numbers be n and the other m.
The sum of two numbers is 40, so
Let n be the larger number, so twice the larger number is , and twice the larger divided by the smaller is .
The quotient is 3 and the remainder 10 when m is the divisor means
Now we have a second equation:
Solve the first equation for n by subtracting m from both sides:
Substitute this expression for n into the first equation:
Multiply both sides by m:
Distribute the 2
Add -80 and -3m to both sides
Collect like terms:
Divide by -5
Substitute your value for m into the first equation:
So the smaller number is 14 and the larger number is 26.
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