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

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Answer 1 · 2018-03-03T06:22:24

Write down what you know first:

We have 2 numbers, number 1 and number 2.

We also know that:

#"number 2" = "5 more than" \ 2 xx "number 1"#

#"number 1 + number 2 = 80"#

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

# {(y = 5 + 2x), (x + y = 80) :}#

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

If

#y = 5 + 2x#

then

#x + (5 + 2x) = 80#

is the same as:

#1x + (5 + 2x) = 80#

Combine like terms:

#5 + 3x = 80#

Solve for #x#:

#3x = 80 - 5#

#3x = 75#

#x = 25#

So

#y = 5 + 2(25)#

#y = 55#