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

User Bates
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2 Answers

6 votes

two numbers are 10 and 6 .

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 .

User PapEr
by
8.6k points
4 votes

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

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.

User Gyan Veda
by
7.7k points

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