Giving 15 points for !

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.

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.'

Step-by-step 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.

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."