# The larger of 2 numbers is 11 less than 3 times the smaller. The sum is 69. what are the numbers?

Mar 8, 2018

color(magenta)(x=20

#### Explanation:

Let the no.s be $x$ and $3 x - 11$

According to the question,

$x + 3 x - 11 = 69$

$4 x - 11 = 69$

$4 x = 69 + 11$

$4 x = 80$

$x = \frac{80}{4}$

color(magenta)(x=20

~Hope this helps! :)

Mar 8, 2018

20 and 49

#### Explanation:

Let's have the smaller number be represented by a variable $x$ and the larger number by $y$. Our first step is to create numerical equations that represent the numbers. The larger number is 11 less than the smaller number if the smaller number is multiplied by 3. Therefore, the first equation is: $y = 3 x - 11$. Our second equation will be $x + y = 69$ since the sum is 69.

Our next step is to substitute one equation into another. That way, we can form an equation with only one variable in it. Let's put our first equation into the second one:

$x + \left(3 x - 11\right) = 69$

From here, all we have to do is simplification:

$x + 3 x - 11 = 69$
$4 x - 11 = 69$
$4 x = 80$
$x = 20$

We have our smaller number, $20$. To find the larger number, plug the smaller number into our second equation and solve for $y$:

$20 + y = 69$
$y = 49$

We now have our larger number $49$.

Mar 8, 2018

The larger number is 49, and the smaller number is 20

#### Explanation:

It's easiest to make the questions into equations so that they are easier to understand.

I'm going to abbreviate "larger number" to L and "smaller number" to S.
When we see: The larger number is 11 less than 3 times the smaller number
We can say: $L = 3 S - 11$

When we see: The sum is 69
We can say: $L + S = 69$

Let's substitute the first equation into the second one. Since $L = 3 S - 11$, we can put it into this equation:

$L + S = 69$
$\left(3 S - 11\right) + S = 69$
$3 S - 11 + S = 69$
$4 S - 11 = 69$
$4 S = 80$
$S = 20$

Now that we know $S$, we can put it into the second equation.
$L + S = 69$
$L + 20 = 69$
$L = 49$

CHECK:
$L = 3 S - 11$
$49 = 3 \left(20\right) - 11$
$49 = 60 - 11$
$49 = 49$ True. We know that our answers are correct.