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 $n$ :

$n = -23 - 4$

$n = -27$