Question

A certain concrete mixture contains 5.00% cement and 7.00% sand. How many kilograms of this mixture and how many kilograms of sand should be combined with 295 kg of cement to make a batch that is 12.0% cement and 14.0% sand? Carry out all calculations.

Answer 1

`3182.2158\ kg` & `307.0408\ kg` respectively

Explanation:

Let `x\ kg` of concrete mixture of `5%` cement & `7%` sand be combined with `y\ kg` of sand & `295\ kg` cement to make a batch of `12%` cement & `14%` sand.

The total amount of final batch/mixture will be

`=x+y+295\ kg`

Now, balancing the amount of cement before & after mixing as follows

`\frac{5}{100}\cdot x+295=\frac{12}{100}(x+y+295)`

`7x+12y=25960\ ........(1)`

Similarly, balancing the amount of sand before & after mixing as follows

`\frac{7}{100}\cdot x+y=\frac{14}{100}(x+y+295)`

`-7x+86y=4130\ ........(2)`

Adding (1) & (2), we get

`7x+12y-7x+86y=25960+4130`

`98y=30090`

`y=307.0408`

setting the value of `y` in (1), we get

`7x+12(307.0408)=25960`

`7x=22275.5104`

`x=3182.2158`

Hence `3182.2158\ kg` of concrete mixture of `5%` cement & `7%` sand should be combined with `307.0408\ kg` of sand & `295\ kg` cement to make a batch of `12%` cement & `14%` sand.