Answer :
Final answer:
To calculate the amount of sand needed for 192 cubic feet of concrete, we set up a proportion based on the given ratio of sand to concrete. Using cross-multiplication, the calculation shows that 90 cubic feet of sand are needed for 192 cubic feet of concrete.
Explanation:
The student is asking for help with a ratio and proportion problem in mathematics related to the amount of sand needed for making concrete. The ratio provided is that 3 3/4 cubic feet (ft³) of sand are needed to make 8 cubic feet of concrete. To find out how much sand would be required to make 192 cubic feet of concrete, we set up a proportion.
First, we begin by converting the mixed fraction to an improper fraction: 3 3/4 ft³ is equal to (3 × 4 + 3) / 4 or 15/4 ft³ of sand. Then, we set up the proportion as follows:
15/4 ft³ sand / 8 ft³ concrete = x ft³ sand / 192 ft³ concrete,
where x represents the amount of sand needed. Cross-multiplication gives us:
15 × 192 = 4 × 8 × x,
Simplifying,
2880 = 32x,
and dividing both sides by 32 gives us:
x = 90.
Therefore, the student would need 90 cubic feet of sand to make 192 cubic feet of concrete.
Learn more about Ratio and Proportion here:
https://brainly.com/question/26974513
#SPJ11
