Question

The sum of two numbers is 16. The total of three times the smaller and twice the larger is 42

Answer 1

two numbers are 10 and 6 .

Step-by-step explanation:

Here we have , The sum of two numbers is 16. The total of three times the smaller and twice the larger is 42 . We need to find the two numbers . Let's fins out:

Let two numbers be x & y so ,

The sum of two numbers is 16

With this info we have following linear equation:

⇒ $x+y=16$

The total of three times the smaller and twice the larger is 42

With this info we have following linear equation:

⇒ $3x+2y=42$

Let's solve these

⇒ $3x+2y=42$

⇒ $x+2(x+y)=42$                     { $x+y=16$ }

⇒ $x+2(16)=42$

⇒ $x=10$

Putting $x=10$ in $x+y=16$ we get:

⇒ $10+y=16$

⇒ $y=6$

Therefore, two numbers are 10 and 6 .

Answer 2

The two numbers are 6 and 10 which sums to 16.

Step-by-step explanation:

It is given that, the sum of two numbers is 16.

Let,

• x be the small number.
• y be the large number.

Therefore, x+y = 16 forms the first equation.

It is given that, the total of three times the smaller and twice the larger is 42.

This means that,

Three times the smaller ⇒ 3x.

Twice the larger ⇒ 2y.

The total of three times the smaller and twice the larger is 42 can be represented as (3x+2y) = 42 which forms the second equation.

The system of equations are :

x+y = 16  --------(1)

3x+2y = 42 -------(2)

Multiply eq (1) by 2, and subtract eq (2) from eq (1),

 2x+2y = 32

-(3x+2y = 42)

  -x      = - 10

Therefore, the value of x is 10.

To find the number y :

Substitute x=10 in eq (1),

10+y = 16

y = 6.

The other number is 6.