Thread: Applied word problems involving fractional equations Mixture problems

1. Applied word problems involving fractional equations Mixture problems

A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.

i was working on this equation which I don't know if it's correct or not

Started with + We add = What we end up with

8 + X = 0.1 ( 40 + X )

2. Re: Applied word problems involving fractional equations Mixture problems

Originally Posted by diehardmath4
A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.

i was working on this equation which I don't know if it's correct or not

Started with + We add = What we end up with

8 + X = 0.1 ( 40 + X )
let $X$ be the amount of zinc that needs to be added in $kg$

$\dfrac{8 + X}{40+8+X} = \dfrac{1}{10}$

$8+X = 0.1(48+X)$

so not quite, you forgot about the initial amount of zinc present in the total.

3. Re: Applied word problems involving fractional equations Mixture problems

Originally Posted by romsek
let $X$ be the amount of zinc that needs to be added in $kg$

$\dfrac{8 + X}{40+8+X} = \dfrac{1}{10}$

$8+X = 0.1(48+X)$

so not quite, you forgot about the initial amount of zinc present in the total.
the zinc alloy must be defined

4. Re: Applied word problems involving fractional equations Mixture problems

Originally Posted by bjhopper
the zinc alloy must be defined
you don't think they mean 10% zinc, 90% copper?

5. Re: Applied word problems involving fractional equations Mixture problems

Originally Posted by romsek
you don't think they mean 10% zinc, 90% copper?
Zinc alloy contains another component. It is left out in this reply.

6. Re: Applied word problems involving fractional equations Mixture problems

The answer the book is giving me is 40 kg

7. Re: Applied word problems involving fractional equations Mixture problems

Zinc alloy contains another component. It is left out in this reply.
Are you reading this as 40 kg of copper and a separate amount of an alloy that contains 8 kg of zinc?

I interpret it as 40 kg of a combined copper & zinc alloy that contains 8 kg zinc $\implies$ 32 kg of copper in the starting 40 kg.

Using my interpretation, the starting copper-zinc alloy has 20% zinc to start with ... adding 40kg more of copper will result in a 10% zinc alloy.

8. Re: Applied word problems involving fractional equations Mixture problems

Originally Posted by diehardmath4
A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.

i was working on this equation which I don't know if it's correct or not

Started with + We add = What we end up with

8 + X = 0.1 ( 40 + X )
ok let's try this again

40kg of an allow made of copper and zinc. 8kg is zinc. 32kg is copper.

You want to add copper to this to obtain a new alloy contain 10% zinc.

$\dfrac{8}{40+X}=0.1$

$40+X=80$

$X=40$

So we need to add $40kg$ of copper.

That gets us $80kg$ total with $8kg$ of zinc, i.e. $10\%$

basically everything Skeeter just said.

9. Re: Applied word problems involving fractional equations Mixture problems

Originally Posted by diehardmath4
A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc. Find the amount of copper which must be added if the manufacturer requires a new alloy containing 10% zinc.
The present 8 kg zinc will represent 10% of total, so total of 80 required.

10. Re: Applied word problems involving fractional equations Mixture problems

Analyze the problem "A parts manufacturer has 40 kg of a copper and zinc alloy which contains 8 kg of zinc", here zinc is $20\%$ of the total.

Since you need new alloy containing $10\%$ zinc. we know that 8 kg of 40 kg is $20\%$, so 8 kg of 80 kg will be $10\%$.

Since you have 32 kg copper, so you need more 40 kg copper to make a new allow containing $10\%$ zinc and total 80kg allow.