78% of a number, P, is 23.4 more than 117% of another number, Q. It is further given

that is 40% of P. Find P and Q.

Step-by-step explanation:

"78% of P" looks like this in an algebraic expression:.78P

"117% of Q" looks like this: 1.17Q

" ... is 23.4 more than [above]" looks like this: [above] + 23.4

Putting that all together in one equation, knowing that the word "is" means "equals":

.78P = 1.17Q + 23.4

From there, we will now use the fact that Q is 40% of P, which looks like this:

Q =.4P

Now, using that substitution:

.78P = 1.17 (.4P) + 23.4 and

.78P =.468P + 23.4 and

.312P = 23.4 so

P = 75

Going back up to what Q is equal to, we will sub in the value of P and solve for Q:

Q =.4P and P = 75, therefore,

Q =.4 (75) so

Q = 30