Question

Hello I have an assignment that I need some help with if you can please assist that would be great thank you.

Answer 1

Let x be the number of ear corns sold and let y be the cost.

Step 1.

We know that the constant of proportionality is given by:

`k=(y)/(x)`

Al's stand.

In this case we know that when they sell 6 ears the cost is 1.50, then we have:

`k=(1.5)/(6)=0.25`

Hence, the constant of proportionality for Al's stand is 0.25

Barbara's stand.

For this stand we have that:

`k=(3.12)/(13)=0.24`

Hence, the constant of proportionality for Barbara's stand is 0.24

Step 2.

Once we have the constant of proportionality we can write the equation for each stand.

Al's stand:

`y=0.25x`

Barbara's stand:

`y=0.24x`

Step 3.

Al's stand table.

If they sell 14 ears, then:

`y=0.25(14)=3.5`

If they sell 21 ears, then:

`y=0.25(21)=5.25`

If the total cost is $50 then:

`\begin{gathered} 50=0.25x \\ x=(50)/(.25)=200 \end{gathered}`

Barbara's stand

If they sell 14 ears:

`y=0.24(14)=3.36`

Is they sell 21 ears:

`y=0.24(21)=5.04`

If the total cost is $49.92 then:

`\begin{gathered} 49.92=0.24x \\ x=(49.92)/(24) \\ x=208 \end{gathered}`

Step 4

The constant of porportionality for this problem gives us the price per ear of corn.

Step 5

Barbara's stand has the better value, this comes from the fact that the constant of proportionality is smaller for this stand; which means that the cost for each ear of corn is less.