Oil that costs 22.50/barrel is mixed with oil that costs 35.00/barrel. how many barrels of each oil should be included in 1250 barrels of mixture that sells for 27.50/barrel?

So 22.5 per barrel

so 22.5
x represents the number of 22.5 barrels

y represents the number of 35 barrels

so
x+y=1250

then find the total cost
1250 barrels
27.5 per so mutiply by 1250 and get 34375 total cost

22.5x+35y=34375

we have 2 senctances
x+y=1250
22.5x+35y=34375

elimination
mulitply first equation by -35 to clear y
-35x-35y=-43750
add to second equation
-35x-35y=-43750
22.5x+35y=34375    +
-12.5x+0y=-9375
-12.5x=-9375
multiply -1
12.5x=9375
divie both sides by 12.5
x=750

subsitute
x+y=1250
750+y=1250
subtract 750
y=500

750 barrells of the 22.5 oil should be included and
500 barrells of the 35 oil should be included