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