One number is four less than a second number. Twice the first is 15 more than 3 times the second. How do you find the numbers?

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Answer 1 · 2016-12-05T17:27:49

The two numbers are #-23# and #-27#

We need to first write this problem in terms of equation and then solve the simultaneous equations.

Let's call the numbers we are looking for #n# and #m#.

We can write the first sentence as an equation like:

#n = m - 4#

And the second sentence can be written as:

#2n = 3m + 15#

Now we can substitute #m - 4# into the second equation for #n# and solve for #m#;

#2(m - 4) = 3m + 15#

#2m - 8 = 3m + 15#

#2m - 2m - 8 - 15 = 3m - 2m + 15 - 15#

#-8 - 15 = 3m - 2m#

#-23 = m#

We can now substitute #-23# for #m# in the first equation and calculate #n#:

#n = -23 - 4#

#n = -27#