Question

the sum of three numbers is 57 if twice the first number is 6 less than the second and the second number is 10 more than the third find the number​

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Given :-

• The sum of three numbers is 57
• Twice the first number is 6 less than the second
• The second number is 10 more than the third number.

To find :-

• The numbers.

Sóĺúťíóń :-

Sum of three numbers = 57.

•°• Let the first number be a

Let the second number be b

Let the third number be c

a + b + c = 57 ----> 1

As per the first condition :-

• Twice the first number is 6 less than the second

First number = a

Second number = b

Twice the first number = 2a

Is 6 less than second = - 6

Let's get it in mathematical equation,

2a = b - 6

2a + 6 = b

•°• b = 2a + 6 ----> 2

As per the second condition :-

• The second number is 10 more than the third

Second number = b

Third number = c

Second number is 10 more = + 10

Let's get it in mathematical equation form,

b = c + 10

b - 10 = c

c = b - 10

From here, we will find the value of c, by substituting the value of b from equation 2,

c = 2a + 6 - 10

c = 2a - 4 -----> 3

Now with the help of these 3 equations let's find out the numbers.

a + b + c = 57

We will substitute the values one at a time, first substutite the value of b from equation 2,

a + 2a + 6 + c = 57

Now, substutite the value of c from equation 3,

a + 2a + 6 + 2a - 4 = 57

Get the terms together,

a + 2a + 2a + 6 - 4 = 57

a + 4a + 2 = 57

5a = 57 - 2

5a = 55

a = $\bf\large\frac{55}{5}$

a = 11

First number, a = 11

Let's now find the value of other numbers using the value of the first number.

Second number :-

• Twice the first number is 6 less than the second

First number = 11

Twice of first number = 2 (11) = 22

Second number = b

Is 6 less than second number = -6

22 = b - 6

22 + 6 = b

28 = b

Second number = 28

For third number :-

• The second number is 10 more than the third

Second number = 28

10 more = + 10

Than third number = c

Let's calculate,

28 = c + 10

28 - 10 = c

18 = c

Third number = c = 18

•°• First number = 11

Second number = 28

Third number = 18

$\bf{\huge{\underline{\boxed{\rm{\red{Verification:}}}}}}$

To be sure whether our answer is right or not, we will add all our resulting answers and check whether we get the sum 57.

a = 11

b = 28

c = 18

Sum = a + b + c

57 = 11 + 28 + 18

57 = 39 + 18

57 = 57

LHS = RHS.

Hence verified.