Question 1132188
i think you're asking how much cement was added to 72 kilograms of the mixture to make the ratio of sand to cement = 6/1 rather than 7/1.


the ratio starts at 7 to 1.


that means 7 parts out of 8 is sand and 1 part out of 8 is cement.


the total number of parts is 8.


72 / 8 = 9


each part is worth 9 kilograms.


7 * 9 = 63 kilograms of sand.


1 * 9 = 9 kilograms of cement.


72 kilograms of mix is equal to 63 kilograms of sand and 9 kilograms.


you add x kilograms of cement to the mixture.


you now have 63 kilograms of sand and 9 + x kilograms of cement.


the ratio of sand to cement is now 6 to 1 rather than 7 to 1.


63 / (9 + x) = 6 / 1


multiply both sides of this equation by (9 + x) to get 63 = 6 * (9 + x) / 1


simplify to get 63 = 54 + 6x


subtract 54 from both sides to get 63 - 54  = 6x


combine like terms to get 9 = 6x


divide both sides by 6 to get 9 / 6 = x which makes x = 1.5 kilograms.


the amount of cement that is added to the mixture is 1.5 kilograms.


you now have 63 kilograms of sand and 9 + 1.5 = 10.5 kilograms of cement.


the new mixture contains 63 kilograms of sand and 10.5 kilograms of cement which is equal to a total mixture of 73.5 kilograms.


the sane to cement ratio is now 63 / 10.5 = 6 / 1.