65% of the children at a party liked chocolate cake. 25 children did not like chocolate cake. We need to find the total number of children at the party.

1. Problem Description

65% of the children at a party liked chocolate cake. 25 children did not like chocolate cake. We need to find the total number of children at the party.

2. Solution Steps

Let $x$ be the total number of children at the party.

65% of the children liked the chocolate cake, so $0.65x$ children liked the chocolate cake.

The percentage of children who did not like the chocolate cake is $100\% - 65\% = 35\%$.

So, 35% of the children did not like the chocolate cake, which is equal to

2

5. Therefore, $0.35x = 25$.

To find the total number of children, we need to solve for $x$:

$x = \frac{25}{0.35} = \frac{25}{\frac{35}{100}} = \frac{25 \times 100}{35} = \frac{2500}{35} = \frac{500}{7} \approx 71.43$

Since the number of children must be an integer, let us calculate $x$ exactly.

$x = \frac{25}{0.35}$

Multiply numerator and denominator by

1

0

0. $x = \frac{2500}{35}$

Divide numerator and denominator by

5. $x = \frac{500}{7}$

This implies 35% of the total number of students is

2

5. Thus, $0.35 x = 25$.

Multiply both sides by 100 to remove decimal.

$35 x = 2500$

Divide both sides by

3

5. $x = \frac{2500}{35}$

Divide numerator and denominator by

5. $x = \frac{500}{7} \approx 71.43$

However, since the number of children must be a whole number, there must be an error in the problem statement. We round to the nearest whole number of

7

1.

Let $x$ = total number of children. Then $0.65x$ liked chocolate cake and 25 did not. So, $x = 0.65x + 25$.

$0.35x = 25$.

$x = \frac{25}{0.35} = \frac{2500}{35} = \frac{500}{7}$.

Since this is not an integer, we need to check the original numbers. If 65% liked it, 35% didn't.

So if 25 is 35%, we have $25 = 0.35x$. Then $x = 25/0.35$.

So $x$ must be about 71, and $0.35(71) = 24.85$ which isn't quite

2

5. Perhaps the 65% is an approximation.

If 25 children is 35% of the total, the total must be $\frac{25}{35/100} = \frac{2500}{35} = \frac{500}{7}$.

The answer MUST be an integer. Let's assume the question stated that 65% liked chocolate cake and 25 did NOT, but the 65% is just an approximation. Let the total be $x$. The fraction who did NOT like is $(1-0.65) = 0.35$. Then $0.35x = 25$, which implies that $x=500/7$. The question must have an error. However, if we round it we get

7

1.

3. Final Answer

500/7