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

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,

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.

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:

⇒

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

With this info we have following linear equation:

⇒

Let's solve these

⇒

⇒                     { }

⇒

⇒

Putting in we get:

⇒

⇒

Therefore, two numbers are 10 and 6 .