Answer:
There are 78 plums and 42 peaches.
Explanation:
Let p = number of plums.
Let e = number of peaches.
The value of the plums is 2p.
The value of the peaches is 3e.
"total cost of plims was 30$ more than the cost of peaches"
2p = 3e + 30
"there are 120 fruits some are plums [...] others are peaches"
p + e = 120
We have a system of simultaneous equations.
2p = 3e + 30
p + e = 120
2p = 3e + 30
p = -e + 120
2p = 3e + 30
+ 3p = -3e + 360
------------------------------
5p = 390
p = 78
p + e = 120
78 + e = 120
e = 42
Answer: There are 78 plums and 42 peaches.
Check:
78 plums cost 78 × $2 = $156
42 peaches cost 42 × $3 = 126
$156 - $126 = $30
The plums do cost $30 more than the peaches.
78 + 42 = 120
The total is indeed 120.
The answer above is correct.