Question

Amaya has an inflatable pool that she filled 34
full for her cousin on a hot summer day. After playing all day, the pool was 310
full. How much of the water was lost? Simplify your answer.(1 point)
Responses

37
3 sevenths

920
9 over 20

1840
18 over 40

16

Answer 1

To find out how much water was lost in Amaya's inflatable pool, we first need to figure out how much water was initially in the pool and how much is left after playing.

Amaya filled the pool \( \frac{3}{4} \) full, which means the volume of water in the pool was:

\[
\frac{3}{4}
\]

After playing, the pool is \( \frac{1}{10} \) full.

Now, we need to subtract the remaining water from the initial amount to find out how much was lost:

\[
\text{Water lost} = \frac{3}{4} - \frac{1}{10}
\]

To perform this subtraction, we need to find a common denominator. The least common multiple of 4 and 10 is 20.

Now converting \( \frac{3}{4} \) and \( \frac{1}{10} \) to have a denominator of 20:

\[
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\]
\[
\frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20}
\]

Now we can subtract:

\[
\frac{15}{20} - \frac{2}{20} = \frac{15 - 2}{20} = \frac{13}{20}
\]

So, the amount of water lost is:

\[
\frac{13}{20}
\]

Now let's check the responses provided:

- \( \frac{37}{7} \) (approximately 5.29)
- \( \frac{920}{20} \) (equivalent to 46)
- \( \frac{1840}{40} \) (which simplifies to 46)
- \( 16 \)

None of these match \( \frac{13}{20} \). It seems the options given do not include the correct answer in simplified form.

Thus, the water lost, simplified, is \(\frac{13}{20}\). Please double-check the problem or provide the correct options so I can help further.