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Determine the quantities (in terms of weight) of ingredients to mix 84 ft\(^3\) of mortar. Given:

- Volume of sand = 3.5 \(\times\) (Volume of cement + Volume of lime)
- Volume of lime = 0.53 \(\times\) Volume of cement

Assume:

- Unit weight of sand in the moist loose condition is 94 pcf
- Unit weight of lime is 40.4 pcf
- Unit weight of cement is 94.2 pcf

Options:

1. Weight of Sand = 7,896.0 lbs, Weight of Cement = 1,477.6 lbs, Weight of Lime = 369.5 lbs
2. Weight of Sand = 8,321.5 lbs, Weight of Cement = 1,533.0 lbs, Weight of Lime = 306.9 lbs
3. Weight of Sand = 7,896.0 lbs, Weight of Cement = 1,477.6 lbs, Weight of Lime = 335.9 lbs
4. Weight of Sand = 8,321.5 lbs, Weight of Cement = 336.2 lbs, Weight of Lime = 369.8 lbs

Which one of the options above is correct?

Answer :

The correct option is Option 1 (top): Weight of Sand = 7,896.0 lbs, Weight of Cement = 1,477.6 lbs, Weight of Lime = 369.5 lbs.

To determine the quantities of ingredients to mix 84 ft^3 of mortar, we need to follow the given information. We start by using the given relationship between the volume of sand, cement, and lime. The volume of sand is stated as 3.5 times the sum of the volume of cement and the volume of lime. This can be expressed as 84 ft^3 = 3.5(Volume of cement + Volume of lime). Next, we are given the relationship between the volume of lime and the volume of cement, which is 0.53 times the volume of cement. Using this information, we can substitute the expression for the volume of lime into the previous equation.

Now that we have the volume of cement, we can calculate the weights of each ingredient. The weight of cement is determined by multiplying its unit weight, which is given as 94.2 pcf, by the volume of cement. Plugging in the calculated values, we find that the weight of sand is approximately 7,896.0 lbs, the weight of cement is approximately 1,477.6 lbs, and the weight of lime is approximately 369.5 lbs. Therefore, the correct option is Option 1 (top): Weight of Sand = 7,896.0 lbs, Weight of Cement = 1,477.6 lbs, Weight of Lime = 369.5 lbs.

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