Question

the difference between the two positive integers is 50 and the ratio of these integers is 1:3 find these integers ​

Answer 1

the difference between the two positive integers is 50 and the ratio of these integers is 1:3 find these integers

The difference between two positive integers is 50. The ratio of these integers is 1:3. What are these integers?

x - y = 50 and x/y = 3/1 (x must be > y in order to get a positive sum.)

x/y = 3/1

cross multiply to get

x = 3y

In x - y =50 replace x with 3y

3y - y = 50

Combine like terms

2y = 50

Divide both sides by 2

y = 25

In x - y = 50 Replace y with 25.

x - 25 = 50

Add 25 to both sides

x = 75

Check:

75-25=50

75/25= 3/1

These integers are 75 and 25.

Have A Happy Day :-)

Since the ratio of the two integers is 1:3, then,

We let x and 3x be the integers.

To determine the integers, we get the difference of the two integers which is 50.

thus,

3x - x = 50

2x = 50

x = 25.

Substituting x by 25 from the the two integers x and 3x.

x = 25 and:

3x = 3(25) = 75

Therefore, the integers are 25 and 75

Let the numbers be x and y.

x/y=1/3 (because the ratio of these integers is 1:3)

This implies that 3x=y

The difference the numbers

y-x(because y is the larger number)=50

Since y=3x

y-x=3x-x=2x

But y-x is equal to 50

This means 2x=50

x=25

y=3x=3*25=75

The numbers are 75 and 25

Let X and Y be the two numbers and Y be greater than X.

The difference of the Integers is

Y - X = 50 => Y = X + 50 -> Equation 1

The ratio of the Integers is ,

X/Y = 1/3 => 3X = Y -> Equation 2

Substituting the value of Y in Equation 2,

3X = X + 50

2X = 50

X =25

Substituting the value of X in Equation 2

Y - 25 = 50

Y = 75

Answer 2

GivEn:

• Difference between two positive integers is 50.
• Ratio of these Integers is 1:3.

⠀

We have to find:

• These Integers

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☯ Let the first positive integer be x.

☯ And, the second positive integer be 3x.

${\underline{\sf{\bigstar\;Now,\; According\;to\; Question\;:}}}$

$:\implies\sf 3x - x = 50$

$:\implies\sf 2x = 50$

$:\implies\sf x = \cancel{ \dfrac{50}{2}}$

$:\implies{\boxed{\frak{\pink{x = 25}}}}\;\bigstar$

Therefore,

• First positive integer, x = 25

• Second positive integer, 3x = 3 × 25 = 75

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• Integers are defined as a number that can be written without a fractional component.

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• For example, 2, 5, 0, and −1086 are integers, while 9.75 and √5 are not.