Richard went shopping and bought a pen, a book and a magazine. The magazine cost ¼ of a book. The pen cost 1/3 of the magazine. If he spent 734.40 pesos, how much did he spend for the pen?
Spent X pesos for the book.
Spent x/4 pesos for the magazine.
Spent 1/3 * x/4 = x/12 pesos for the pen.
x + x/4 + x/12 = 734.40,
Multiply both sides 12:
12x + 3x + x = 8812.8,
X = ?
Let's assign variables to the costs of the book, magazine, and pen.
Let b be the cost of the book.
The magazine cost 1/4 * the cost of the book = b/4.
The pen cost 1/3 * the cost of the magazine = (b/4) / 3 = b/12.
The total amount Richard spent is b + b/4 + b/12 = (12b + 3b + b) / 12 = 16b / 12.
Given that he spent 734.40 pesos, we can set up the equation (16b / 12) = 734.40.
Multiply both sides of the equation by 12 to get rid of the fraction: 16b = 12 * 734.40.
Divide both sides of the equation by 16 to solve for b: b = (12 * 734.40) / 16.
Calculate b: b = 550.80 pesos.
The cost of the pen is b/12 = 550.80 / 12 = 45.90 pesos.
Therefore, Richard spent 45.90 pesos for the pen.
To determine how much Richard spent on the pen, we need to calculate the costs of the book and the magazine first.
Let's assign variables to the costs of the book (B), the magazine (M), and the pen (P).
According to the given information:
- The magazine cost 1/4 of a book, so M = (1/4)B.
- The pen cost 1/3 of the magazine, so P = (1/3)M.
We also know that the total amount Richard spent is 734.40 pesos.
Therefore, we can set up the equation: B + M + P = 734.40.
Now, let's substitute the values of M and P into the equation:
B + (1/4)B + (1/3)((1/4)B) = 734.40.
Let's simplify the equation by finding a common denominator:
B + (1/4)B + (1/12)B = 734.40.
Combining the terms with B:
(1 + 1/4 + 1/12)B = 734.40.
Finding the common denominator of 4 and 12, which is 12, we get:
(12/12 + 3/12 + 1/12)B = 734.40.
Simplifying:
(16/12)B = 734.40.
Converting the mixed number into an improper fraction:
(4/3)B = 734.40.
To solve for B, we divide both sides of the equation by 4/3:
B = (734.40) / (4/3).
Dividing a number by a fraction is equivalent to multiplying it by the reciprocal of the fraction. So, we have:
B = (734.40) * (3/4).
Calculating:
B = 550.80.
Now that we know the cost of the book, we can find the cost of the magazine by substituting B into the first equation:
M = (1/4) * 550.80.
M = 137.70.
Lastly, to find the cost of the pen, we substitute M into the second equation:
P = (1/3) * 137.70.
P = 45.90.
Therefore, Richard spent 45.90 pesos for the pen.
b + p + m = 734.4
m = b / 4 ... b = 4 m
p = m / 3 ... m = 3 p ... b = 12 p
substitute to find the solution