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Two Numbers Differ by 5. If their Product is 336, then the Sum of the Two Numbers is?

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Explanation

  • Two numbers differ by 5.
  • Their product is 336.
  • The sum of the two numbers will be figure out in this way.

Let suppose the numbers are y and z.

The difference between two numbers is 5

y – z = 5 ________ (i)

The product of these numbers is 336.

yz = 336 ________ (ii)

By solving equation (i) and (ii) simultaneously, we can easily find out the value of y (y = 21) and z (z = 16) in order to find out the sum (y + z = 21 + 16 = 37).

To Find

Sum = ?

Solution

Let suppose

Integers are y and z.

According to the given conditions

y – z = 5 ________ (i)

yz = 336

y = 336/z ________ (ii)

Putting y = 336/z in equation (i)

336/z – z = 5

336 – z2 = 5z

z2 + 5z – 336 = 0

z2 + 21z – 16z – 336 = 0

z(z + 21) – 16(z + 21) = 0

(z – 16)(z + 21) = 0

z – 16 = 0           &                z + 21 = 0

z = 16 (possible)           &                z = -21 (not possible)

Put z = 16 in equation (i)

y – 16 = 5

y = 5 + 16

y = 21

Required Sum = 16 + 21 = 37answer

Conclusion

Two numbers differ by 5. If their product is 336, then the numbers are 21 and 16 and there sum will be 37.

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