A farmer at a farmers' market creates a sign to show equivalent rates of the cost of tomatoes per pound. If she were to add another row for 10 pounds of tomatoes, what number would be in the numerator for its corresponding rate?
Number of pounds:
0.5
4
7
Cost in Dollars
1.75
14.00
24.50
Rate
$1.75/0.5lb.
$14.00/4lb.
$24.50/7lb.
If the farmer were to add another row for 10 pounds of tomatoes, the numerator for its corresponding rate would be $35.00.
To find the numerator for the corresponding rate of 10 pounds of tomatoes, we can use proportionality.
First, let's look at the rates given for different quantities of tomatoes:
- $1.75 for 0.5 pounds of tomatoes
- $14.00 for 4 pounds of tomatoes
- $24.50 for 7 pounds of tomatoes
To find the cost for 10 pounds of tomatoes, we can set up a proportion:
0.5 pounds / $1.75 = 10 pounds / x
We can then cross-multiply and solve for x:
0.5x = 10 * $1.75
0.5x = $17.50
Dividing both sides of the equation by 0.5, we find:
x = $17.50 / 0.5
x = $35
Therefore, the numerator for the corresponding rate of 10 pounds of tomatoes would be $35.
To find the number that would be in the numerator for the rate of 10 pounds of tomatoes, we can set up a proportion using the given rates.
Let's set up the proportion:
Cost in Dollars / Number of pounds = Rate
Using the given rates:
$1.75/0.5lb. = $14.00/4lb. = $24.50/7lb.
So, we can write the proportion as:
$1.75/0.5 = $14.00/4 = $24.50/7
Now, we can find the value for 10 pounds of tomatoes by cross multiplying the second and third terms of the proportion:
($14.00/4) * (10) = $24.50/7 * (10)
This simplifies to:
$35.00 = $35.00
Therefore, the number that would be in the numerator for the rate corresponding to 10 pounds of tomatoes is $35.00.