Question

The sum of the double of a number and 5 times of another number is

120. When thrice of the first number and 4 times of the second were

added, the sum is 117. Find the numbers​

Answer 1

Given :- The sum of the double of a number and 5 times of another number is 120. When thrice of the first number and 4 times of the second were added, the sum is 117. Find the numbers ?

Solution :-

Let us assume that, the first number is x and second number is y.

Than,

→ Double of first number + 5 times of second number = 120

→ 2x + 5y = 120 ---------- Eqn.(1)

Also,

→ thrice of first number + 4 times of second number = 117

→ 3x + 4y = 117 --------- Eqn.(2)

Multiply Eqn.(1) by 3 and Eqn.(2) by 2 and than subtracting Eqn.(2) from Eqn.(1) we get,

→ 3(2x + 5y) - 2(3x + 4y) = 3 * 120 - 2 * 117

→ 6x + 15y - 6x - 8y = 360 - 234

→ 7y = 126

dividing both sides by 7,

→ y = 18. (Ans.)

Putting value of y in Eqn.(1),

→ 2x + 5*18 = 120

→ 2x + 90 = 120

→ 2x = 120 - 90

→ 2x = 30

dividing both sides by 2,

→ x = 15. (Ans.)

Hence, The first number is 15 and second number is 18.

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