Brian spent 1/3 of his money on 5 pens and 11 erasers. The cost of each pen is 3 times the cost of each eraser. He bought some more pens with 3/4 of his money. How many pens did Brian buy altogether?
Since 1/3 + 3/4 > 1, I am assuming that by "3/4 of his money" you mean 3/4 of the 2/3 he had left, or 1/2 of his total money.
the cost p = 3e
5p+11e = x/3
so 5p + 11p/3 = x/3
26p/3 = x/3
now, 1/2 = 3/2 * 1/3, so
3/2 * 26p/3 = 13p
He bought 13+5 = 18 pens
Cost of 5 pens = 5u
Cost of 11 pens = 11v
5u + 11v = x/3
Since, u = 3v
-> 15v + 11v = x/3
-> 26v = x/3
-> v = x/3*26 = x/78 -> 78v
-> cost of an eraser = x/78
-> cost of a pen = 3 * x/78 = x/26
He bought some more pens with 3/4 of his money.
After spending x/3 money on 5 pens and 11 erasers, Brian left with x - x/3 = 2x/3
money. : 3/4 of 2x/3 = 3/4 * 2x/3 = x/2
He spent x/2 money on some more pens.
Since, x = 78v, v = u/3 where u
is cost of a pen
-> x = 78 * u/3 = 26u
: x/2 = 26u/2 = 13u
Since u is cost of a pen,
13u is cost of 13 pens
-> Extra pens = 13
: Total number of pens
= Extra number of pens + 5 pens
= 13 + 5
= 18
-> Brian buy 18 pens altogether.
To find out how many pens Brian bought altogether, we need to break down the problem step by step.
First, let's find the cost of each pen relative to the erasers:
Let's assume the cost of each eraser is x.
Therefore, the cost of each pen would be 3x since it is 3 times the cost of each eraser.
Now, let's find out how much money Brian spent on 5 pens and 11 erasers:
The number of erasers Brian bought is 11, and the cost of each eraser is x.
So, the total cost of the erasers is 11x.
The number of pens Brian bought is 5, and the cost of each pen is 3x.
So, the total cost of the pens is 5 * 3x = 15x.
Brian spent 1/3 of his money on the pens and erasers, so the total cost of the pens and erasers is 1/3 of his money.
Let's assume Brian's total money is M.
Therefore, 1/3 * M = 15x + 11x = 26x.
So, 26x is equal to 1/3 of Brian's money. Now we can find the value of x:
26x = 1/3 * M
To isolate x, divide both sides of the equation by 26:
x = (1/3 * M) / 26
Now, let's find out how much money Brian has left after buying the pens and erasers:
Brian spent 1/3 of his money, so he has 2/3 of his money remaining.
The remaining amount is equal to 2/3 * M.
Brian then spent 3/4 of his remaining money on more pens.
So, the money spent on more pens is 3/4 * (2/3 * M).
To find out how many pens Brian bought altogether, we need to divide the money spent on more pens by the cost of each pen (3x):
Number of pens bought = (3/4 * (2/3 * M)) / (3x)
Now we have a formula for the number of pens Brian bought altogether. You can substitute the value of x (from the earlier equation) and the value of M (Brian's total amount of money) into the formula to get the answer.