The sum of two numbers is 68. Five times the smaller number is 16 more than the larger. Find the two numbers.

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24-11-2017
Mathematics

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The sum of two numbers is 68. Five times the smaller number is 16 more than the larger. Find the two numbers.

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jamiexx jamiexx · Answer 1 · 2017-11-24T04:09:40+01:00

We can use simultaneous equations to solve that. Which means we can solve 2 unknown numbers from 2 algebraic formulas.

Let the smaller number be y, and the larger number be z.

Now list the 2 equations from the given info.

y + z = 68 (equation 1)
5y = 16 + z (equation 2)

From (1),
y = 68 - z (equation 3)

Substitute (3) into (2).
5 (68-z) = 16 + z
340 - 5z = 16 + z
324 = 6z
z = 54

Now substitute z = 54 back into (1).
y + 54 = 68
y = 14

Therfore the 2 numbers are 14 and 54