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A fuel depot blends premium and regular gasoline to fill a 600-gallon order that must be exactly 92 octane. Premium is 95 octane and regular is 87 octane. The blend is then sold at $4.20 per gallon for the premium portion and $3.60 per gallon for the regular portion. What is the total revenue from the order?
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Correct answer
D
First find the blend split by octane. Let p be the number of premium gallons, so 600 − p is the number of regular gallons. Since the blend must average to 92 octane: (95p + 87(600 − p)) ÷ 600 = 92. Multiply out: 95p + 52,200 − 87p = 55,200, so 8p = 3,000 and p = 375. That leaves 600 − 375 = 225 regular gallons.
Sanity check on the split: 95 is 3 above the 92 target and 87 is 5 below it, so the gallons split 5 : 3 in favor of premium, which matches 375 premium to 225 regular.
Once the split is fixed, apply the two prices to the two portions: revenue = 375 × $4.20 + 225 × $3.60 = $1,575 + $810 = $2,385. Both steps are required. The octane weighted average fixes the split, and only then does the dual-rate pricing give the revenue.
So (D) $2,385 is correct.
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