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Lyza is selling kakanin before she goes to school.
She sells putubumbong and bibingka at 10.50 pesos and 12.75 pesos per slice, respectively.
Her total earnings today is 389.25 pesos.
If she sold more putubumbong than bibingka, what is the total number of kakanin sold? *
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In this problem, we have only one equation for two unknowns, which are "p" and "b",
the number of putubumbong and bibingka, respectively
p*10.50 + b*12.75 = 389.25. (1)
So, it seems, that there are many solutions.
But we have two additional restrictions.
First, the solutions "p" and "b" must be integer numbers.
Second, we are looking for the solution in non-negative integer numbers, where "p" is greater than "b".
It provides the UNIQUENESS of the solution.
So, we write from equation (1)
b = ,
We run p = 1, 2, 3, . . . , and we are looking for positive integer values of b, which we obtain from this formula.
The solutions in integer positive numbers are (p,b) = (14,19) and /or (31,5)
Of these two pairs, only the pair (p,b) = (31,5) has the value of p (31) greater than b (5).
So, p + b = 31 + 5 = 36 is the solution to the problem. ANSWER
Solved.
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The way to facilitate the required calculations is to use Excel software, if you have it in your computer.
Then you can make your calculations pleasant, instead having them torturous.