Before it started to rain, Amnar cut 16

Question

of the grass and Aayush cut 13
of the grass. Which statement is true?

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(1 point)
Responses

The boys cut almost the whole yard.
The boys cut almost the whole yard.

Together the boys cut three-fourths of the yard.
Together the boys cut three-fourths of the yard.

The boys cut exactly half of the yard.
The boys cut exactly half of the yard.

Together the boys did not cut half of the yard.

Answer 1

To determine which statement is true, we need to compare the portions of grass cut by Amnar and Aayush.

Amnar cut \( \frac{16}{\text{some total}} \) of the yard and Aayush cut \( \frac{13}{\text{some total}} \) of the yard. Assuming the total area of the yard is represented by 1 (or 100%), we can add the portions cut by both boys.

Let's denote the total area of the yard as 1 (or 100%). We then consider the fractions of the yard each boy cut.

1. Combined area cut by both boys: \[ \text{Total} = \frac{16}{\text{Total}} + \frac{13}{\text{Total}} = \frac{16 + 13}{\text{Total}} = \frac{29}{\text{Total}} \]

2. Looking for equal comparisons:

   • If the total yard is taken as 1 (whole yard):
     • \( \frac{29}{\text{Total}} = \frac{29}{1} = 29 \)

3. Comparing with the statements:

   • If they cut more than half of the yard, then \( \frac{29}{1} > \frac{1}{2} \), which is not useful because it exceeds total yard.
   • Further, evaluating the fractions:
     • Three-fourths of the yard is \( \frac{3}{4} \) or 0.75, and if we think of \( \frac{29}{x} \):
       • They are both cutting significant portions, confirming the portion cut is likely significant.

In conclusion, since \(\frac{16 + 13}{Total} = \frac{29}{Total}\) is not clearly qualifying for the exact half, but they cut more than half of the yard:

Thus, the correct response must be: Together the boys cut three-fourths of the yard.

Given that they cut proportions leading toward significantly high quantities, thus validating the statement equivalently.