Question

# 1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?

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## Answer to a math question 1. A jeweler has two gold bars, with 80% purity and the other with 95% purity. How much of each must be melted to obtain a 5 kilo ingot with 86% purity?

Gerhard
4.5
Para resolver este problema, podemos utilizar una ecuación basada en la cantidad de oro y la pureza del oro en cada lingote.

Sea $x$ la cantidad de oro que se va a fundir del lingote con 80% de pureza $en kilos$.
Entonces, la cantidad de oro que se va a fundir del lingote con 95% de pureza sería $$5-x$$ kilos.

La ecuación para la pureza del oro en el lingote resultante sería:
0.8x + 0.95$5-x$ = 0.86 \cdot 5

Resolviendo esta ecuación, paso a paso:

0.8x + 4.75 - 0.95x = 4.3
0.8x - 0.95x = 4.3 - 4.75
-0.15x = -0.45
Dividiendo ambos lados por $-0.15$ para despejar $x$:
x = \frac{-0.45}{-0.15}

Simplificando la expresión:
x = 3

Por lo tanto, se deben fundir 3 kilos del lingote con 80% de pureza y $5-3=2$ kilos del lingote con 95% de pureza para obtener un lingote de 5 kilos con un 86% de pureza.

\textbf{Respuesta:} Se deben fundir 3 kilos del lingote con 80% de pureza y 2 kilos del lingote con 95% de pureza para obtener un lingote de 5 kilos con un 86% de pureza.

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