16Hit1600
AlgebraEasySolve a system by elimination in context

Algebra practice question

A food truck owner buys bags of flour and jugs of oil, where every bag of flour costs the same amount and every jug of oil costs the same amount. One week the owner paid $41 for 2 bags of flour and 3 jugs of oil. The next week the owner paid $68 for 2 bags of flour and 6 jugs of oil.

What is the cost, in dollars, of one bag of flour?

Answer: 7

Let f be the cost of a bag of flour and j the cost of a jug of oil: 2f + 3j = 41 and 2f + 6j = 68. Subtracting eliminates f: 3j = 27, so j = 9. Then 2f + 3(9) = 41 gives 2f = 14 and f = 7. A student who stops after finding the oil price answers 9; one who forgets to divide 2f = 14 by 2 answers 14.

Common wrong answers

If you answered 9
That's j, the cost of one jug of oil. Substitute it back: 2f + 27 = 41, so f = 7.
If you answered 14
You correctly found 2f = 14 but stopped there — divide by 2 to get one bag of flour: $7.
If you answered 27
That's 3j, the total from subtracting the two equations, not a single item's cost. Divide by 3 to get j = 9, then solve for f = 7.

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