Question

Hank has 50 peso, 200 peso and 500 peso bills in his wallet. He has five less 200 bills as 50 bills, and half as many 500 bills as 200 bills. If he has Php 6250 in all, how many of each denomination does he have?

Answer 1

For an amount of 6250 Peso, Hank have the quantities of the following denominations: 2503 bills of 50 peso, 2498 bills of 200 peso and 1249 bills of 500 peso.

How to apply systems of linear equations in real life equations

In this question we must translate the statement of the problem into mathematical expressions and then we must solve the resulting system. We need three equations that describe the quantities of 50 peso, 200 peso and 500 peso bills:

y = x - 5     (1)

0.5 · y = z    (2)

x + y + z = 6250     (3)

The solution of the system of linear equations is described below:

x = 2503, y = 2498, z = 1249

For an amount of 6250 Peso, Hank have the quantities of the following denominations: 2503 bills of 50 peso, 2498 bills of 200 peso and 1249 bills of 500 peso. $\blacksquare$

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