5g + 18-7g + 4g = 8
1 answer:
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Answer: n = 10.
Step-by-step explanation:
In the bag, we have n counters.
4 of the counters are red.
the rest are blue, then we have:
(n - 4) blue counters.
Now, the probability that Ross takes a blue counter from the bag is equal to the quotient between the number of blue counters (n - 4) and the total number of counters, n
Then the probability is:
p1 = (n - 4)/n
Now he draws another, and it must be blue again, then we can calculate the probability in the same way as above, but he already take a blue counter, so the number of blue counters is (n - 5) and the total number of counters is (n - 1)
The probability of this event is:
p2 = (n - 5)/(n - 1)
The joint probability (the probability that Ross takes two blue counters) is equal to the product of the individual probabilities, and we know that this is equal to 1/3, then we have the equation:
1/3 = ( (n - 4)/n)*((n - 5)/(n - 1))
Now let's solve this for n.
n*(n - 1)/3 = (n - 4)*(n - 5)
(n^2 - n)/3 = n^2 - 4*n - 5*n + 20
n^2 - n = 3*(n^2 - 9*n + 20)
n^2 - n = 3*n^2 - 27*n + 60
0 = (3*n^2 - n^2) - 27*n + n + 60
0 = 2*n^2 - 26*n + 60
The two solutions of this equation can be found with Bhaskara's equation:
Then the two solutions are:
n = (26 - 14)/4 = 3
This is not an option, because we know for sure that we have 4 red counters, then this option can be discarded.
The other solution is:
n = (26 + 14)/4 = 40/4 = 10
Then we have n = 10, 10 counters in total.
We are told to use simple interest rate. Formula for this is:
Where:
A= total accumulated amount (principal + interest)
P= principal
r= yearly percentage rate
t= number of years
We need to save $19500 for the first year at a college. This is the amount we will have at the account after five years. In our case this is A.
Principal is the amount we need to put into savings to get the total amount needed. In our case this is P.
Yearly percentage rate is the percentage by which our savings increase at the end of a year. In our case this is r.
t is number of years that we are holding our money on the bank account.
To solve this problem we will assume that we are putting same amount each month on the bank account.
We are given:
A=$19500
P=?
r=1.5%
t=5 years
First step is to transform r into decimal number:
Now we get back to our formula and we solve it for P:
We insert numbers and we get our principal:
We need to put $18139.53 into savings to get required amount after 5 years or 5*12=60months. Assuming that we put same amount each month into savings we need to put
This is our solution for this problem. This is closest to the amount we would need to put in real life. In real life we would earn interest onto interest and our monthly amount would be smaller.
Where:
A= total accumulated amount (principal + interest)
P= principal
r= yearly percentage rate
t= number of years
We need to save $19500 for the first year at a college. This is the amount we will have at the account after five years. In our case this is A.
Principal is the amount we need to put into savings to get the total amount needed. In our case this is P.
Yearly percentage rate is the percentage by which our savings increase at the end of a year. In our case this is r.
t is number of years that we are holding our money on the bank account.
To solve this problem we will assume that we are putting same amount each month on the bank account.
We are given:
A=$19500
P=?
r=1.5%
t=5 years
First step is to transform r into decimal number:
Now we get back to our formula and we solve it for P:
We insert numbers and we get our principal:
We need to put $18139.53 into savings to get required amount after 5 years or 5*12=60months. Assuming that we put same amount each month into savings we need to put
This is our solution for this problem. This is closest to the amount we would need to put in real life. In real life we would earn interest onto interest and our monthly amount would be smaller.