Find two numbers whose sum is 34, and whose difference is 32.?

Question

Find two numbers whose sum is 34, and whose difference is 32.

What is the larger number?_______
What is the smaller number?________

Answer 1

x + y = 34- - - - - -Equation 1
x - y = 32- - - - - - Equation 2
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2x = 66

2x / 2 = 66 / 2

x = 66 / 2

x = 33

Insert the x value into equation 1
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x + y = 34

33 + y = 34

33 + y - 33 = 34 - 33

y = 1

insert the y value into equation 1

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Check for equation 1

x + y = 34

33 + 1 = 34

34 = 34

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Check for equatio 2

x - y = 32

33 - 1 = 32

32 = 32

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Both equations balance

The solution set is { 33, 1 }

The larger number is 33

The smaller number is 1

- - - - - - - - - -s-

Answer 2

let the no's be = x and y
equation 1 equation 2
x + y = 34 x - y = 32

solving equation 1 and 2, we get
2x = 66
x = 33

> x + y = 34
33 + y = 34
y = 1

the larger no is 33
the smaller no is 1

Answer 3

Wrong. The previous answer is wrong. The question never implied whether the two numbers are integers or not, therefore it can be a fraction. We can set two equations were xy = P (largest product) x+y=45 subsituting x=45-y to the 1st equation, 45y-y^2=P we can simplify this to -(y^2-45y)=P After this we need to complete the square -(y^2-45y+2025/4)+2025/4=P -(y-45/2)^2+2025/4=P now lets say (y-45/2) is a variable z. - z^2 + 2025/4 = P would come out. and now we need to think logically. For P to have the highest number z would have to equal zero because any negative number added to a positive number would decrease the answer, in this case, P. Therefore, z has to be 0 making y=45/2 and P as 2025/4 The incorrect answer was 506, but it turns out to be 506.25 *mindblown*

Answer 4

Let the larger number is m, the smaller number is n.
It is known that
m + n = 34 --> 1st Equation
m - n = 32 --> 2nd Equation
1st + 2nd gives us
2m = 66
m = 33
1st - 2nd gives us
2n = 2
n =1

So, the larger number is 33, the smaller number is 1.

Answer 5

first number is x and the 2nd number is x+32

2x+32=34
2x-32=34-32
2x=2
x=1
x+32=33

Larger number is 33 smaller number is 1

Answer 6

Equation 1:

x + y = 34

Equation 2:

x - y = 32

From eq. 1: y = 34-x (this is eq. 3)

substituting this in eq. 2:

x - (34-x) = 32
x - 34 + x = 32
2x -34 = 32
2x = 66 (after adding 34 to both sides)
x = 33 (after dividing both sides by 2)

Larger number = 33

subsituting x=33 in eq. 3

y = 34 - 33

y = 1

smaller number = 1

Answer 7

33 and 1

Answer 8

33 and 1

Answer 9

Largest number-31
Smaller Number-1

The method is Simultaneous Equations
X+Y=34
X-Y+32

Answer 10

33 +1 = 34
33-1= 32

your numbers are 33 and 1