Oooooh, these sorts of problems ised to give me fits!
4a + 3p = 0.9
3a + 4p = 0.85
This looks like a case for elimination! Which should we eliminate, a or p? It doesn't matter, but I'm gonna do a. The LCM of 4 and 3 is 12, so how can we get 12 and -12?
We can multiply the top by 3 and the bottom by -4, or -3 and 4. Again, either will work.
3(4a + 3p) = 3(0.9)
-4(3a + 4p) = -4(0.85)
12a + 9p = 2.7
-12a - 16p = -3.4
Now, if we add the two equations together, 12a + (-12a) = 0, so a cancels out!
-7p = -0.7
p = 0.1
Hey, one pear costs 10 cents.
4a + 3(0.1) = 0.9
4a + 0.3 = 0.9
4a = 0.6
a = 0.15
Aaaaand, one apple costs 15 cents.
Hope this helps!
