Let's break down the problem step-by-step to determine how many pizzas were left in the end.
1. Initial Pizzas:
Hanny made 7 pizzas initially.
2. Pizzas Given to Her Neighbor:
She gave [tex]\( 2 \frac{1}{2} \)[/tex] or 2.5 pizzas to her neighbor.
3. Pizzas Eaten by Her Children:
Hanny's 3 children each ate [tex]\( \frac{1}{4} \)[/tex] of a pizza. Therefore, the total amount of pizza eaten by the children is:
[tex]\[
3 \times \frac{1}{4} = \frac{3}{4} = 0.75 \text{ pizzas}
\][/tex]
4. Remaining Pizzas After Giving to Neighbor and Children:
Subtract the pizzas given away and eaten by the children from the initial pizzas:
[tex]\[
7 - 2.5 - 0.75 = 3.75 \text{ pizzas}
\][/tex]
5. Additional Pizzas Made by Hanny:
After that, Hanny made an additional 4 pizzas. Therefore, the total number of pizzas now is:
[tex]\[
3.75 + 4 = 7.75 \text{ pizzas}
\][/tex]
6. Pizzas Broken:
[tex]\( \frac{3}{5} \)[/tex] of these 7.75 pizzas broke and had to be thrown away. The number of pizzas that broke is:
[tex]\[
\frac{3}{5} \times 7.75 = 4.65 \text{ pizzas}
\][/tex]
7. Pizzas Left in the End:
The number of pizzas left after discarding the broken ones is:
[tex]\[
7.75 - 4.65 = 3.10 \text{ pizzas}
\][/tex]
8. Express the Remaining Pizzas as a Mixed Number:
We need to convert 3.10 pizzas into a mixed number in its simplest form. We observe that:
[tex]\[
3.10 \text{ pizzas} = 3 + 0.10 \text{ pizzas}
\][/tex]
[tex]\( 0.10 \)[/tex] can be simplified as [tex]\( \frac{1}{10} \)[/tex].
Therefore, the mixed number is:
[tex]\[
3 \frac{1}{10}
\][/tex]
Thus, the number of pizzas left in the end is:
[tex]\[
\boxed{3 \frac{1}{10}}
\][/tex]
Looking at the answer choices provided:
(A) [tex]\( 7 \frac{3}{20} \)[/tex]
(B) [tex]\( 3 \frac{1}{10} \)[/tex]
(C) [tex]\( 7 \frac{1}{10} \)[/tex]
(D) [tex]\( 3 \frac{3}{20} \)[/tex]
The correct answer is [tex]\( 3 \frac{1}{10} \)[/tex], which matches with option (B).
