Question

The ratio of copper and zinc in an alloy is 9:8. If the weight of the zinc in the alloy is 9.6kg, find the weight of copper in the alloy

Answer 1

Answer:

Solution. Weight of zinc = 9.6 kg. ⇒ x = 9 × 9.6 8 = 9 × 1.2 = 10.8 kg.

Step-by-step explanation:

Answer 2

Given:

• The ratio of copper and zinc in an alloy = 9 : 8.
• The weight of zinc in the alloy = 9.6 kg.

To find:

• The weight of copper in the alloy.

Solution:

Let's consider the weight of copper in the alloy as 'm' kg. So, as per the given data, the weights of copper and zinc are in the ratio 9 : 8 which can be written in fractional form as 9/8, where the value of 8 equals 9.6 kg and the value of 9 equals 'm' kg. Now, this can be written as an equation:

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \dfrac{9}{8} = \dfrac{m}{9.6} }}}$

Solving this equation results in the value of 'm', i.e, the weight of copper in the alloy. Let's solve it!

$\longmapsto{ \sf{ \dfrac{9}{8} = \dfrac{m}{9.6}}} \\ \\ \longmapsto{ \sf{9(9.6) = m(8) \: \: \: \: \: \: \: \: \: \bigg ( \because \: Cross - multiplication \bigg )}} \\ \\ \longmapsto{ \sf{86.4 = 8m}} \\ \\ \longmapsto{ \sf{ \dfrac{86.4}{8} = m}} \\ \\ \longmapsto \boxed{ \boxed{ \frak { \pmb{ \red{10.8 \: \sf{kg }= m}}}}}$

Verification:

On substituting the value of 'm' in the equation formed:

$\longmapsto{ \sf{ \dfrac{9}{8} = \dfrac{ m}{9.6} }} \\ \\ \longmapsto{ \sf{ \dfrac{9}{8} = \dfrac{10.8}{9.6} }} \\ \\ \longmapsto { \sf{ \dfrac{9}{8} = \dfrac{10.8 \times 5}{9.6 \times 5} }} \\ \\ \longmapsto{ \sf{ \dfrac{9}{8} = \dfrac{ \cancel{54}}{ \cancel{48}} }} \\ \\ \longmapsto \boxed{ \sf{ \dfrac{9}{8} = \dfrac{9}{8} }}$

L.H.S equals R.H.S, hence the value of 'm' is correct!

$\\ \therefore \underline{ \frak { \pmb{The \: weight \: of \: copper \: in \: the \: alloy \: is \: \pink{10.8 \: kg }. }}}$

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