SOLUTION: Amina bibi has prepared masonry mixture with sand and cement in a ratio of measurement 7:1. But after the brick-work it is seen that 72 kg of mixture remains. She has added more ce
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Question 1132188: Amina bibi has prepared masonry mixture with sand and cement in a ratio of measurement 7:1. But after the brick-work it is seen that 72 kg of mixture remains. She has added more cement with this mixture and the ratio of measurement of sand to cement becomes 6:1. Let’s work out the total quantity of cement she has mixed. Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 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.
So, we have 72 kg of the mixture containing sand and cement in the ratio 7:1.
It means that there are 7+1 = 8 parts of the equal mass; each mass is = 9 kilograms.
So, there are 7*9 = 63 kilograms of the sand and 9 kilograms of the cement in the original mixture.
We want to add "x" kilograms of the cement to get the ratio sand to cement 6:1.
= ====>
63 = (9+x)*6
63 = 54 + 6x
x = = = 1.5 kilograms of cement to add. ANSWERCHECK. = = 6. ! Correct !
