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

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Let one of the numbers be n and the other m.

The sum of two numbers is 40, so n%2Bm=40

Let n be the larger number, so twice the larger number is 2n, and twice the larger divided by the smaller is 2n%2Fm.

The quotient is 3 and the remainder 10 when m is the divisor means 3%2B10%2Fm

Now we have a second equation:

2n%2Fm=3%2B10%2Fm

Solve the first equation for n by subtracting m from both sides:

n=40-m

Substitute this expression for n into the first equation:

cartoon%282red%28n%29%2Fm=3%2B10%2Fm%2C2%2Ared%28%2840-m%29%29%2Fm=3%2B10%2Fm%29

Multiply both sides by m:

2%2840-m%29=3m%2B10

Distribute the 2

80-2m=3m%2B10

Add -80 and -3m to both sides

-2m-3m=10-80

Collect like terms:

-5m=-70

Divide by -5

m=14

Substitute your value for m into the first equation:

cartoon%28n%2Bred%28m%29=40%2Cn%2Bred%2814%29=40%29
n=26

So the smaller number is 14 and the larger number is 26.