Paul mixes cement with sand. He uses 3 3/4 kilograms of cement and 1/2 kilogram more sand than cement. He needs 10 kilograms of the mixture. Does he have enough mixture? If yes, how much more does he have and if no, how much more does he need?
Yes, he has enough mixture. He has 11 1/2 kilograms of the mixture, which is 1 1/2 kilograms more than he needs.
To determine whether Paul has enough mixture, we first need to calculate how much sand he used, and then we can find the total weight of the mixture.
Paul used 3 3/4 kilograms of cement, which is equal to 3 + 3/4 = 15/4 kilograms of cement.
Next, we can find out how much sand he used. It is mentioned that he used 1/2 kilogram more sand than cement. So, the weight of sand he used is 15/4 + 1/2 = (15 + 2) / 4 = 17/4 kilograms of sand.
To find the total weight of the mixture, we add the weight of cement and sand: 15/4 + 17/4 = 32/4 = 8 kilograms.
Therefore, Paul has 8 kilograms of the mixture. However, he needs 10 kilograms of the mixture, which means he is short by 10 - 8 = 2 kilograms.
In conclusion, Paul does not have enough mixture. He needs an additional 2 kilograms of the mixture.
To find out if Paul has enough mixture, we need to add the weights of cement and sand.
Weight of cement = 3 3/4 kilograms = 3 + 3/4 = 12/4 + 3/4 = 15/4 kilograms.
Weight of sand = 1/2 kilogram more than cement = 15/4 + 1/2 = 15/4 + 2/4 = 17/4 kilograms.
Total weight of cement and sand = weight of cement + weight of sand = 15/4 + 17/4 = 32/4 = 8 kilograms.
Paul needs 10 kilograms of the mixture. Since 8 kilograms is lesser than 10 kilograms, Paul does not have enough mixture.
He needs 10 - 8 = 2 kilograms more of the mixture.