Question

If group of people rented the boat for ₱3000 sharing the cost equally. If there have been one more person in the group, each person paid ₱100 less. How many people in group originally?

Answer 1

Answer:

There are 5 people in the group

Step-by-step explanation:

Let there are $N$ people

Total cost of renting the boat = ₱3000

Cost of renting on each = $\frac{3000}{N}$

If there were $N+1$ people then the cost of renting on each

$=\frac{3000}{N+1}$

According to the question, this cost is 100₱ less than the previous cost

Therefore,

$\frac{3000}{N+1}+100=\frac{3000}{N}$

$\implies \frac{3000}{N}-\frac{3000}{N+1}=100$

$\implies 3000(\frac{1}{N}-\frac{1}{N+1})=100$

$\implies 3000(\frac{N+1-N}{N(N+1)})=100$

$\implies \frac{30}{N(N+1)})=1$

$\implies N^2+N=30$

$\implies N^2+N=30$

$\implies N^2+N-30=0$

$\implies N^2+6N-5N-30=0$

$\implies N(N+6)-5(N+6)=0$

$\implies (N+6)(N-5)=0$

$\implies N=-6,5$

but N cannot be negative

Therefore, $N=5$

Thus, there are 5 people in the group.

Hope this helps.

Answer 2

Answer:

Number of people in the group originally = 5

Step-by-step explanation:

In the question,

Let the number of people in the group originally be = n

So,

Amount rented for the boat = 3000

Therefore, Price per person is given by,

$\frac{3000}{n}$

Now,

The number of people has increased by 1 more.

So,

Number of people = n + 1

So,

Amount divided per person is given by,

$\frac{3000}{n+1}$

The difference in the amount per person is = 100.

So,

$\frac{3000}{n}=\frac{3000}{n+1}+100\\So,\\\frac{3000}{n}-\frac{3000}{n+1}=100\\\frac{3000(n+1)-3000n}{n(n+1)}=100\\\frac{3000}{n(n+1)}=100\\So,\\n^{2}+n-30=0\\(n+6)(n-5)=0\\n=5$

Therefore, the number of people originally is given by,

n = 5