Question

5. Find two numbers such that the sum of twice the first and thrice
the second is 92, and four times the first exceeds seven times the second
by 2.
​

Answer 1

Answer:

The sum of twice the first and thrice the second is 92, and four times the first exceeds seven times the second by 2. Let the first number be x and the second number be y. Hence, the first number is 25 and the second number is 14.,

Answer 2

Let x and y be the two numbers.

2x + 3y = 92. -----eqn i

4x = 7y + 2

4x - 7y = 2. -----eqn ii

4 * eqn (i):

8x + 12y = 368. ---- eqn iii

2 * eqn (ii):

8x - 14y = 4. ---eqn iv

eqn (iii) - eqn (iv):

26y = 364

y = 364/26

= 14

Substituting in eqn (ii):

4x - 7(14) = 2

4x - 98 = 2

4x = 2 + 98

= 100

x = 100/4

= 25

Therefore, the numbers are:

x = 25 and y = 14

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