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Sagot :
Answer:
El niño gastó [tex]\frac{8}{15}[/tex] y le quedó [tex]\frac{7}{15}[/tex] del ahorro.
Explanation:
Sea [tex]m[/tex] la cantidad total inicial de su ahorro. A continuación, transformamos cada oración en una expresión matemática:
(i) Un niño gasta [tex]\frac{1}{5}[/tex] de su ahorro inicial:
[tex]p_{1} = \frac{1}{5}\cdot m[/tex] (1)
(ii) Luego, gasta [tex]\frac{2}{3}[/tex] de su ahorro actual:
[tex]p_{2} = \frac{2}{3}\cdot (m-p_{1})[/tex] (2)
[tex]p_{2} = \frac{2}{3}\cdot \left(m-\frac{1}{5}\cdot m)[/tex]
[tex]p_{2} = \frac{2}{3}\cdot \frac{4}{5}\cdot m[/tex]
[tex]p_{2} = \frac{8}{15}\cdot m[/tex]
Ahora, la porción remanente del ahorro es:
[tex]p_{3} = m - p_{2}[/tex]
[tex]p_{3} = \frac{7}{15}\cdot m[/tex]
El niño gastó [tex]\frac{8}{15}[/tex] y le quedó [tex]\frac{7}{15}[/tex] del ahorro.
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