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Varvara68 [4.7K]
3 years ago
14

a storeroom 21 feet long, 15 feet wide, and 11 feet high was enlarged to a length of 25 feet and a width of 17 feet. how many cu

bic feet of storage space were thus added?​
Mathematics
1 answer:
xenn [34]3 years ago
7 0
<h2>1210 cubic feet</h2>

Step-by-step explanation:

       Initial dimensions of the storeroom were 21\text{ }ft length, 15\text{ }ft width and 11\text{ }ft height.

       The room is in the shape of a cuboid. Volume of a cuboid = V=l\times b\times h, where l,b,h are the length, width and height of the cuboid.

       So, Volume of storeroom initially = 21\text{ }ft\text{ }\times15\text{ }ft\text{ }\times11\text{ }ft\text{ }=3465\text{ }ft^{3}\text{ }

       Finally, the length was increased to 25\text{ }ft and width to 17\text{ }ft.

       Final volume of storeroom = 25\text{ }ft\text{ }\times 17\text{ }ft\text{ }\times 11\text{ }ft\text{ }=4675\text{ }ft^{3}\text{ }

       Increase in volume = 4675\text{ ft}^{3}-3465\text{ ft}^{3}=1210\text{ ft}^{3}

∴ 1210 cubic feet of storage was added.

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Answer:

3 liters of 15% and 2 liters of 10%

Step-by-step explanation:

You can set up a table that says the number of liters multiplied by the percent juice equals total percent of juice in L liters:

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That is the main set up for the table.  We will put in values for the percent juice right away, because they were given to us.  Remember that percentages need to be expressed as decimals in order to use them in equations.

              L     *       % juice       =        %L

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___________________________________

13%                           .13

Easy enough so far.  We know that the 15% juice canned juice contains 15% juice.  No secrets there at all.  We also made a row for the mixture that needs to be 13% juice.  Next we know that the total amount of the mixture has to be 5 liters.  If we mix one juice with another and the total has to be 5 liters, then we have an unknown amount of one juice, and 5 - that unknown amount of the other juice.  Filling in we have:

             L      *      % juice       =       %L

15%        x                   .15

10%      5 - x                .10

______________________________

13%         5                   .13

Our equation tells us that we have to multiply the L times the % to fill in that last column:

             L      *      % juice      =       %L

15%        x     *          .15           =      .15x

10%      5-x    *          .10          =     .10(5 - x)

__________________________________

13%         5      *        .13           =     .65

We are told from the problem we are adding the 2 juices to get the mixture, so we will add the rows in the last column and set it equal to .65:

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Let's multiply everything by 100 to get rid of all those decimals:

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x = 3

That means that we need 3 liters of the canned juice that is 15% juice.

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