Question
A cake weighs 900 grams. Ivori cuts it into four pieces for her friends. The biggest piece is as heavy as the three others altogether. What's the weight of the biggest piece?
Answers
Answered by
GPT-4o mini
Let's denote the weight of the biggest piece as \( x \) grams. Since the biggest piece weighs as much as the three other pieces combined, we can say:
\[
x = y_1 + y_2 + y_3
\]
where \( y_1 \), \( y_2 \), and \( y_3 \) are the weights of the three smaller pieces.
Since the total weight of the cake is 900 grams, we can write:
\[
x + y_1 + y_2 + y_3 = 900
\]
Given the first equation where \( y_1 + y_2 + y_3 = x \), we can substitute into the second equation:
\[
x + x = 900
\]
This simplifies to:
\[
2x = 900
\]
Now, divide both sides by 2 to find \( x \):
\[
x = \frac{900}{2} = 450 \text{ grams}
\]
Therefore, the weight of the biggest piece is \( \boxed{450} \) grams.
\[
x = y_1 + y_2 + y_3
\]
where \( y_1 \), \( y_2 \), and \( y_3 \) are the weights of the three smaller pieces.
Since the total weight of the cake is 900 grams, we can write:
\[
x + y_1 + y_2 + y_3 = 900
\]
Given the first equation where \( y_1 + y_2 + y_3 = x \), we can substitute into the second equation:
\[
x + x = 900
\]
This simplifies to:
\[
2x = 900
\]
Now, divide both sides by 2 to find \( x \):
\[
x = \frac{900}{2} = 450 \text{ grams}
\]
Therefore, the weight of the biggest piece is \( \boxed{450} \) grams.