r. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice a
s much as potatoes. To determine the unit price for each item, his daughter sets up and solves the system of equations shown. 6p + 3n = 18 and 2n = p 6(2n) + 3n = 18 12n + 3n = 18 15n = 18; n = $1.20 Onions cost $1.20 per pound. Analyze the daughter’s solution. Which statements are true? Check all that apply. The equation 2n = p should be 2p = n. The equation 6p + 3n = 18 should be 6n + 3p = 18. The actual cost of the onions is $3.00 per pound. Potatoes cost $0.60 per pound. Potatoes cost $1.50 per pound. Potatoes cost $2.40 per pound.
The wording "onions cost twice as much as potatoes" is understood to mean the cost per pound of onions (n) is equal to two times the cost per pound of potatoes (2p). Then the appropriate equation would be ...
2p = n
Then the solution is ...
6p +3(2p) = 18
12p = 18
p = 18/12 = 1.50
n = 2p = 2(1.50) = 3.00
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The equation should be 2p = n; onions cost $3.00 per pound; potatoes cost $1.50 per pound.
