A bottle with a cork costs 10 kopecks, while the bottle itself is 9 kopecksmore expen

[12jpayne]

Hi

I am trying to do some word questions and need help.

A bottle with a cork costs 10 kopecks, while the bottle itself is 9 kopecksmore expensive than the cork. How much does the bottle without the corkcost?

A spoon of wine is poured from a barrel of wine into a (not full) glassof tea. After that, the same spoon of the (inhomogeneous) mixture from theglass is taken back into the barrel. Now both in the barrel and in the glassthere is a certain volume of the foreign liquid (wine in the glass and tea in thebarrel). In which is the volume of the foreign liquid greater: in the glass or inthe barrel?

 

[Otis]

What have you tried thus far?

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The first exercise can be solved using a system of equations.

Let B = price of bottle

Let C = price of cork

The exercise states that their sum is 10 and that their absolute difference is 9. This information yields two equations.

Did you try a similar approach?

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The second exercise does not state any volumes, so we may assume that any chosen volumes would lead to the same conclusion. Pick some volumes, and reason out what happens.

Here's a similar example: Starting with 100ml of cream and 100ml of coffee, transfer 10ml of cream into the coffee. You now have 90ml of pure cream remaining, and you have 110ml of a coffee-cream mixture.

Next, transfer 10ml of the coffee-cream mixture back to the pure cream. You now have 100ml of two different mixtures; one mixture is mostly cream containing a wee bit of coffee, and the other mixture is mostly coffee containing a wee bit of cream.

Is there more cream in that coffee or more coffee in that cream?

To find out, we can use the given volumes to calculate the related percentages.

After the first transfer, calculation ought to reveal that the coffee-cream mixture contains 90.9091% coffee and 9.0909% cream (percents rounded to four places).

Clearly, these percentages of coffee and cream comprise the 10ml of mixture in the second transfer. In other words, the second transfer moves 9.0909ml of coffee and 0.9091ml of cream back into the 90ml of pure cream (percentages rounded).

Examine the math of what happened:

100ml coffee + 10ml cream - 9.0909ml coffee - 0.9091ml cream

90ml cream + 9.0909ml coffee + 0.9091ml cream

Calculate and compare the ending ratios of coffee:cream and cream:coffee.

What do you conclude? :cool: