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# The second of two numbers is 5 more than twice the first. Their sum is 80. How do you find the numbers?

Mar 3, 2018

Write down what you know first:

#### Explanation:

We have 2 numbers, number 1 and number 2.

We also know that:

• $\text{number 2" = "5 more than" \ 2 xx "number 1}$
• $\text{number 1 + number 2 = 80}$

Let's name number 1 $x$ and let's name number 2 $y$.

$\left\{\begin{matrix}y = 5 + 2 x \\ x + y = 80\end{matrix}\right.$

Now, substitute your $y$ value into your 2nd equation.

If

$y = 5 + 2 x$

then

$x + \left(5 + 2 x\right) = 80$

is the same as:

$1 x + \left(5 + 2 x\right) = 80$

Combine like terms:

$5 + 3 x = 80$

Solve for $x$:

$3 x = 80 - 5$

$3 x = 75$

$x = 25$

So

$y = 5 + 2 \left(25\right)$

$y = 55$

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