Are the ratios 25/45 and 15/27 proportional? Explain and show your work (2 points)
A 10-acre field produced 750 bushels of corn. At that rate, ho much corn be produced at a 14-acre field? Show all of your work. (2 points)
Are the ratios 8/12 and 10/25 proportional? Explain.
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To determine if the ratios 25/45 and 15/27 are proportional, we need to check if their cross products are equal. The cross product is obtained by multiplying the numerator of one ratio with the denominator of the other ratio.
For the first comparison:
Cross product of 25/45 = 25 * 27 = 675
Cross product of 15/27 = 15 * 45 = 675
Since the cross products are equal, the ratios 25/45 and 15/27 are proportional.
Now, let's move on to the second question:
To find out how much corn can be produced on a 14-acre field at the same rate as the 10-acre field, we can set up a proportion.
Given information:
10 acres produce 750 bushels of corn
14 acres = ?
We can set up the proportion as follows:
10 acres / 750 bushels = 14 acres / x bushels
To solve for x, the number of bushels produced on the 14-acre field, we can cross multiply and solve for the unknown variable:
10 acres * x bushels = 750 bushels * 14 acres
10x = 10500
Divide both sides by 10:
x = 10500 / 10
x = 1050
Therefore, at the same rate, a 14-acre field would produce 1050 bushels of corn.
Simplify each fraction.
Solve this proportion.
10/750 = 14/x