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math 210

by Shane Trattles
(Sauk Centre)











































Scott and Greg were asked to add two whole numbers. Instead, Scott subtracted thw two numbers and got 10, and Greg multiplied them and got 651. what was the correct sum?

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Jan 16, 2011
Math 210 – Word Problem - Part II (Trial & Error Solution)
by: Staff



PART II: using TRIAL & ERROR to solve the problem


To solve for both numbers using trial and error:

Since both X and Y must be positive INTEGERS, you can factor the 651 in the 2nd equation to determine what possibilities exist.

2nd Equation: X * Y = 651

X * Y = 651

Factor the number 651

651 = 1 * 3 * 7 * 31

There are only three possibilities for the two numbers: (31, 21), (93, 7), (217, 3)

Now use equation 1 to find the two numbers whose difference is 10:

Equation 1: X – Y = 10

X – Y = 10

31 – 21 = 10

This is the only combination which can be subtracted to get a difference of 10.

X = 31
Y = 21

The final answer is the same answer we arrived at using equations: 31 + 21 = 52




Thanks for writing.


Staff
www.solving-math-problems.com



Jan 16, 2011
Math 210 – Word Problem - Part I (Equation Solution)
by: Staff



PART I: using EQUATIONS to solve the problem

The question:
by Shane Trattles
(Sauk Centre, MN)

Scott and Greg were asked to add two whole numbers.

Instead, Scott subtracted the two numbers and got 10, and Greg multiplied them and got 651.

What was the correct sum?

The answer:

1. Scott and Greg were asked to add two whole numbers.

Whole numbers are the set of numbers: 0, 1, 2, 3, …

(The set of whole numbers does not contain any negative numbers.)

Since they were asked to add two whole numbers, the final answer will also be a WHOLE NUMBER (whole numbers are “closed” under addition).

This problem can be solved using trial and error. It can also be solved using equations.

I’ll demonstrate both methods, beginning with the use of equations.


2. Variable names:

X = 1st number
Y = 2nd number

3. Scott subtracted the two numbers and got 10.

X – Y = 10

4. Greg multiplied the same numbers and got 651.

X * Y = 651


5. These are the two equations you can use to solve the problem:

X – Y = 10
X * Y = 651

6. Solve for X & Y using the substitution method:

X – Y = 10

Add Y to each side of the 1st Equation

X – Y + Y= 10 + Y

X + 0 = 10 + Y

X = 10 + Y

X = Y + 10

Since (Y + 10) stands for X, substitute (Y + 10) for each X in the 2nd equation, then solve for Y.

X * Y = 651

(Y + 10) * Y = 651

Y* Y + 10 * Y = 651


Y^2 + 10 * Y = 651

Y^2 + 10Y = 651

Subtract 651 from each side of the equation

Y^2 + 10Y – 651 = 651 - 651

Y^2 + 10Y – 651 = 0

Factor the result

(-Y – 31) * (-Y + 21) = 0


Look at the factored equation.

In order for the equation to equal zero, either (-Y – 31) must = 0, or (-Y + 21) must = 0, or both.

Solve each of the two equations for Y.

1st possibility: -Y – 31 = 0

-Y – 31 = 0

Add Y to each side of the equation

-Y + Y – 31 = 0 + Y

– 31 = Y

Y = – 31. Although -31 is a valid solution for the equation, this SOLUTION WILL NOT WORK. Both the 1st number and the 2nd number must be whole numbers (positive integers) to answer your original question. – 31 is a negative integer.

2nd possibility: -Y + 21 = 0

-Y + 21 = 0

Again, add Y to each side of the equation.

-Y + Y + 21 = 0 + Y

0 + 21 = 0 + Y

21 = Y

Y = 21. This solution is not only a solution to the equation, it is a positive integer. 21 IS THE SOLUTION for the 2nd number.

Substitute 21 for Y in the 2nd equation:

2nd Equation: X * Y = 651

X * Y = 651

Since we already know that Y (the 2nd number) is = 21, we can substitute 21 for every Y that appears in the 2nd equation.

X * Y = 651

X * 21 = 651

Divide each side of the equation by 21

(X * 21)/21 = 651/21

X * (21/21) = 651/21

X * (1) = 651/21

X * 1 = 651/21

X = 651/21

X = 31

X = 31. This solution is a positive integer. 31 is the value of the 1st number.

The two numbers are:

X = 31 (the 1st number)
Y = 21 (the 2nd number)

7. What was the correct sum? (This is your original question.)

X + Y = 31 + 21 = 52


The final answer: the sum of the two numbers is 52.

Feb 14, 2014
SOLVING MATH NEW
by: SIBONISO MDLALOSE

IF YOU WANT TO SOLVE Dx(2x+18).you can solve it like that;exponent of x,multiply by the coeffient of x and to the coeffient of x you have to substrat or minus 1 .and you know that the derivative of the constant 18=0.therefore Dx=2

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