Question

The sum of two numbers is 10 and their sum is four times the smaller number. Find the two numbers

Answer 1

Given

The sum of two numbers is 10 and their sum is four times the smaller number

We Find

The Required Numbers

We Know

☆ Let the 1st number be x

☆ Let the 2nd number is 4x because this is four time bigger than value of x

According to the question

4x + x = 10

5x = 10

x = 10 / 5

x = 2

So, The numbers is :-

X = 2 × 1 = 2

4x = 4 × 2 = 8

So, Value of X and 4x is 2 , 8.

Verification

We put the values , so :-

4x + x = 10

8 + 2 = 10

10 = 10

LHS ≈ RHS

Hence , The required numbers is 2 , 8.

$\:$

Answer 2

Correct Question :

• The difference of two numbers is 10 and their sum is four times the smaller number. Find the two numbers

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Given :

• The difference of two numbers is 10
• Their sum is four times the smaller number

To Find :

• The two numbers

Solution :

• Let one number be x and another number which is small be y

• Now , according to the question :

$\leadsto {\boxed{\sf{\red{ x\:-\:y\:=\:10}}}} --- eq(1)$

$\leadsto \sf x\:+\:y\:=\:4y$

$\leadsto \sf x\:=\:4y\:-\:y$

$\leadsto \sf x\:=\:3y$

$\leadsto {\boxed{\sf {\red{x\:-\:3y\:=\:0}}}} --- eq(2)$

• Subtract both the equations :

$\leadsto \sf x\:-\:y\:-(x\:-\:3y)\:=\:10\:-\:0$

$\leadsto \sf x\:-\:y\:-\:x\:+\:3y\:=\:10$

$\leadsto \sf 2y\:=\:10$

$\leadsto \sf y\:=\: \dfrac{10}{2}$

$\leadsto {\boxed{\sf{\red{y\:=\: 5}}}}$

• Smaller number is y = 5
• Greater number is x = 3y = 3(5) = 15

↪ Greater number is 15 whereas smaller number is 5

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Verification :

$\star\: \sf Difference\:of\:both\:no.(s)\:=\:10$

$\leadsto \sf x\:-\:y\:=\:10$

$\leadsto \sf 15\:-\:5\:=\:10$

$\leadsto \sf 10\:=\:10$

• LHS = RHS , hence , Verified

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