Category: Algebra
"Published in Newark, California, USA"
Milagros bought a number of baskets of calamansi for ₱ 60. She sells them at a gain of ₱ 0.50 a basket and has as her profit the amount received for the last 6 baskets sold. How much did she pay per basket of calamansi?
Solution:
The given word problem is about money and investment problem in which buying, selling, and profit are involved. Let's analyze the given word problem as follows:
Let x = be the number of baskets of calamansi
y = be the price or cost of calamansi per basket
If the word problem says "Milagros bought a number of baskets of calamansi for ₱ 60.", then the working equation which is her capital or investment is
If the word problem says "She sells them at a gain of ₱ 0.50 a basket...", then the working equation which is her sales is
If the word problem says "....and has as her profit the amount received for the last 6 baskets sold.", then the working equation which is her profit is
If you put all equations together, then the final working equation is
But 
Hence, the above equation becomes
By using the completing the square method, the value of x which is the number of baskets of calamansi is
We need to choose the positive sign since we want to get the number of baskets of calamansi.
Substitute the value of x to the first given equation, we have
Therefore, the cost of a basket of calamansi is ₱ 2.00.
Category: Algebra
"Published in Newark, California, USA"
The product of two consecutive integers is 106 less than twice the square of the next larger integer. Find the numbers.
Solution:
The first thing that we need to do is to analyze the given problem as follows:
Let x = be the first consecutive integer
x + 1 = be the second consecutive integer
x + 2 = be the third consecutive integer
If the word problem says "The product of two consecutive integers is 106 less than twice the square of the next larger integer.", then the working equation is
From the working equation, the value of x which is the first consecutive integer is
If you equate each factor to zero, then the values of x are -14 and 7.
Therefore, the three consecutive integers are -14, -13, and -12 or 7, 8, and 9.
Category: Algebra
"Published in Newark, California, USA"
In 1964, Thelma bought two lots at ₱ 9,600 each. One lot contains 40 square meters more than the other but costs ₱ 12 less per square meter. Find the area of each lot.
Solution:
The given problem is about finding the area of two lots in which Thelma bought. The other lot has a bigger area but cheaper price. The prices of both lots are the same. Let's analyze the given word problem as follows:
Let x = be the area of Lot #1
y = be the price of Lot #1 per square meter
x + 40 = be the area of Lot #2
y - 12 = be the price of Lot #2 per square meter
The working equation for Lot #1 is
The working equation for Lot #2 is
But 
Hence, the above equation becomes
By using the completing the square method, the value of x is
Since area is always a positive value, then we need to choose the positive sign. Therefore, the area of Lot #1 is
and the area of Lot #2 is 160 m² + 40 m² = 200 m².
