# The sum of two numbers is 53. Three times the smaller number is equal to 19 more thhan the larger number. Determine the numbers.

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let the numbers be x and y:

the sum of the two numbers is 53

==> x + y = 53 ........(1)

Also, given that 3 times the smaller number is 19 more than the larger:

==> 3x = 19 + y

==> 3x - y = 19 ..........(2)

Now let us use the elimination method to solve:

Add (1) and (2):

==> 4x = 72

==> x= 72/4

**==> x= 18**

Now tocalculate y:

x+ y = 53 ==> y= 53- x

==> y= 53- 18

**==> y= 35**

**Then the numbers are 18 and 35**

We can set up two equations to help us find the two numbers.

First, because the two numbers add up to 53, we can say

x + y = 53

Next, if x is the smaller number, we can say that

3x = y + 19

Now, we can find a value for y by using the first equation.

y = 53 - x.

Now, let's substitute that in to the second equation:

3x = 53 - x + 19

4x = 72

**x = 18**

If x = 18 and 53 - x = y, then **y = 35**

We have 2 numbers and we'll note the smaller number as x.

If the sum of the numbers is 53, we could write the second number as y = 53 - x.

Now, we'll write mathematically the phrase: "Three time the first is five more then twice the second"

3 times the smaller number = 3x

19 more = 19 +

19 more than the larger number = 19 + 53 - x

Let's join them:

3x = 19 + 53 - x

We'll add x both sides and we'll combine like terms:

4x = 72

We'll divide by 4:

**x = 18**

Now, we'll calculate the second number:

y = 53 - 18

**y = 35**

sum of two numbers = 53.

x and 53-x be the these numbers:

3 times smaller number = larger number +19.

3x = 53-x+19

Add x:

3x+x = 53+19 = 72

3x = 72

x = 72/3 = 24.

Other number = 53-24 = 29