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
Harish Chandra Rajpoot
Jul 28, 2018

#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.

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