Question

The sum of two positive integers is 351. The integers are in the ratio 2:7. Find the integers.​

Answer 1

Answer :–

• The first integer is 78.
• The other integer is 273.

Given :–

• Sum of two positive integers = 351.
• The integers are in the ratio = 2 : 7.

To Find :–

• The both integers.

Solution :–

Let,

The first integer be 2x.

The other integer be 7x.

According to the question,

First integer + Other integer = Sum of two positive integers

• Sum of two positive integer = 351.

$\hookrightarrow 2x + 7x = 351$

$\hookrightarrow 9x = 351$

$\hookrightarrow x = \dfrac{\cancel{351}}{\cancel9}$

$\hookrightarrow x = \dfrac{\cancel{117}}{\cancel3}$

$\hookrightarrow x = \dfrac{39}{1}$

$\hookrightarrow x = 39$

Now,

The first integer = 2x = 2 × 39 = 78.

The other integer = 7x = 7 × 39 = 273.

Hence,

• The first integer = 78.
• The other integer = 273.

Check :–

Here the values are,

• The first integer = 78.
• The other integer = 273.
• Sum of both two integers = 351.

According to the question,

First integer + Other integer = Sum of both integers.

$\hookrightarrow 78 + 273 = 351$

$\hookrightarrow 351 = 351$

Since, the L.H.S. and the R.H.S. are equal.

So, the answer is correct.