Question 213082
Let  a  = #  apples,,,,and  p=# pencils
.
$ @ Grocery = 3.40 +1.19 +.15a = 4.59 + .15a
.
$@ Drug Store = 4.99 + .10 p
.
but  amounts  are  equal
.
4.59 + .15 a = 4.99 + .10p
.
.15a - .10 p = .40,,,,,,,mult  by  10
.
15a -10p = 40,,,,,divide  by  5
.
3a -2p =8,,,,,  this  is  one  eqn  for  two  unknown
.
Lets  examine  potential  answers
.
#a,,,,,#p,,,,,,,,,,,,,,,,,,,,,,,,,,,#p,,,,,#a
.
0,,,,,,-4,,,,,,,,,,,,,,,,,,,,,,,,,,,,0,,,,,,,8/3
1,,,,,,-2.5,,,,,,,,,,,,,,,,,,,,,,,,,,1,,,,,,,,10/3
2,,,,,,-1,,,,,,,,,,,,,,,,,,,,,,,,,,,,2,,,,,,,,4,,,,,,1st  practical  answer
3,,,,,,1/2
4,,,,,,,2,,,,,,1st  practical  answer
.
therefore we  can  say  that  we  must  buy  at  least  4  apples,and  2 pencils
in  the  ratio  2  apples  for  each  4  pencils
.
. check,,  4.99 + .10(2) = 4.59 + .15(4) = 5.19,,,0k