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We will call the two numbers X and Y.

1) X + Y = 102

2) X - Y = 42

3) Rearrange the second equation ---> X = Y + 42 and plug into the first.

4) (Y + 42 ) + Y = 102

5) 2Y + 42 = 102

6) 2Y = 60

7) Y = 30 *

8) Plug into the second equation ---> X - 30 = 42 (so X = 42+ 30)

9) X = 72 *

10) 72 is the answer.

Q: Two numbers have a sum of 102 Their difference is 42 What is the larger of the two numbers?

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Suppose x is the larger number Then the smaller number is x - 26 Their sum is x + (x - 26) which is 102 So 2x - 26 = 102 or 2x = 128 so that x = 64

There are no two consecutive numbers that add or multiply to 102.

102 has three different prime factors so there are no TWO numbers as required by the question.

24 + 16 = 40

Any two of its factors

Related questions

Suppose x is the larger number Then the smaller number is x - 26 Their sum is x + (x - 26) which is 102 So 2x - 26 = 102 or 2x = 128 so that x = 64

There are no two consecutive numbers that add or multiply to 102.

0.8 is larger. The difference between the two numbers is 0.072.

100 and 363, 101 and 364, 102 and 365, ... Take your pick!

The two numbers would be 102 and 104. (102+104=206)

You get the difference between the sizes of the two numbers without regard for their sign, and the difference has the same sign as the larger of the two original numbers.

-9 and -3 or 3 and 9

102 has three different prime factors so there are no TWO numbers as required by the question.

The difference of two squares is equivalent to the sum, times the difference, of the numbers that are squared. In symbols: a2 - b2 = (a + b)(a - b) Here is an example with numbers: 102 - 92 = (10+9)(10-9)

24 + 16 = 40

Any two of its factors

It can be, but only if the smaller number is a factor of the larger number.For example:Factors of 102: 1 2 3 6 17 34 51 102Factors of 34: 1 2 17 34The GCF of 102 and 34 is 34