Math  /  Algebra

Question19 A mixture of sand and cement is to be used to plaster a wall. In the original mixture, the ratio of sand to cement by weight is 3:13:1. Given that the weight of sand used is 9 kg, (a) write down the weight, in kg, of cement used in the original mixture. _______ kg (1) It is decided to use the same weight of cement but to change the ratio of sand to cement by weight to 5:15:1 for a new mixture. (b) Calculate the weight of sand, in kg, that has to be added to the original mixture to make the new mixture.

Studdy Solution

STEP 1

1. The original mixture has a sand to cement ratio of 3:13:1.
2. The weight of sand used in the original mixture is 9 kg.
3. The weight of cement used in the original mixture needs to be determined.
4. The new mixture has a sand to cement ratio of 5:15:1.
5. The same weight of cement is used in the new mixture.
6. We need to calculate the additional weight of sand needed for the new mixture.

STEP 2

1. Determine the weight of cement in the original mixture.
2. Calculate the total weight of sand needed for the new mixture.
3. Determine the additional weight of sand required for the new mixture.

STEP 3

Determine the weight of cement in the original mixture.
Given the ratio 3:13:1, for every 3 parts of sand, there is 1 part of cement. Since 9 kg of sand is used, the weight of cement is:
Weight of cement=9kg3=3kg \text{Weight of cement} = \frac{9 \, \text{kg}}{3} = 3 \, \text{kg}

STEP 4

Calculate the total weight of sand needed for the new mixture.
The new ratio is 5:15:1, meaning for every 5 parts of sand, there is 1 part of cement. Since the weight of cement remains 3 kg, the weight of sand needed is:
Weight of sand in new mixture=5×3kg=15kg \text{Weight of sand in new mixture} = 5 \times 3 \, \text{kg} = 15 \, \text{kg}

STEP 5

Determine the additional weight of sand required for the new mixture.
The original mixture has 9 kg of sand. The new mixture requires 15 kg of sand. Therefore, the additional sand needed is:
Additional sand needed=15kg9kg=6kg \text{Additional sand needed} = 15 \, \text{kg} - 9 \, \text{kg} = 6 \, \text{kg}
The weight of cement used in the original mixture is 3 \boxed{3} kg. The additional weight of sand needed for the new mixture is 6 \boxed{6} kg.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord