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.

1 Answer

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.