Question

Giving 15 points for help!

Mr. Yi buys vegetables at a market. He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18. Onions cost twice as 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.

Answer 1

Explanation:

1,3,5

Answer 2

Answer: The correct statements are 'The equation 2n = p should be 2p = n' , 'The actual cost of the onions is $3.00 per pound' and 'Potatoes cost $1.50 per pound.'

Explanation:

Here, p represents cost of one potato and n represents the cost of one onion.

And, According to the question, He purchases 6 pounds of potatoes, p, and 3 pounds of onions, n, for $18.

Therefore, 6p +3n = 18 ------(1)

And, Onions cost twice as much as potatoes.

Therefore, n= 2p ---------(2)

Putting the values of n from 2) in equation 1),

we get, 6p+3(2p)=18

⇒6p+6p=18 ⇒ 12p =18 ⇒ p = 1.5 dollar.

Thus cost of one potato= $1.5

And cost of one onion = $ 2× 1.5= $ 3.00

Thus with help of above explanation we can say that Options first, third and fifth are correct.