Each week, Best Foot Forward orders 8 boxes of socks for every 3 cases of shoes. This rate is constant.
1. If the store orders 96 boxes of socks one week, how many cases of shoes would it order
2. This week, Best Foot Forward ordered 27 cases of shoes. How many boxes of socks did the store order?
3. Identify the personality for the boxes of socks to the cases of shoes enter your answer as a fraction
4. identify the constant of proportionality for the cases of shoes to the boxes of socks enter your answer as a fraction
To answer these questions, we need to understand the constant rate or proportionality between the boxes of socks and cases of shoes. Let's start by calculating the ratio or fraction that represents the relationship between these quantities.
Let's assume that "x" represents the number of cases of shoes, and "y" represents the number of boxes of socks.
1. We know that Best Foot Forward orders 8 boxes of socks for every 3 cases of shoes. So, the ratio is 8 boxes of socks / 3 cases of shoes. To find out how many cases of shoes would be ordered when 96 boxes of socks are ordered, we can set up a proportion:
8 boxes of socks / 3 cases of shoes = 96 boxes of socks / x cases of shoes
To solve for x, we can cross-multiply and then solve for x:
8x = 96 * 3
8x = 288
x = 288 / 8
x = 36
Therefore, when 96 boxes of socks are ordered, the store would order 36 cases of shoes.
2. Similarly, if Best Foot Forward ordered 27 cases of shoes, we can set up the proportion as follows:
8 boxes of socks / 3 cases of shoes = y boxes of socks / 27 cases of shoes
Again, cross-multiply and solve for y:
8 * 27 = 3y
216 = 3y
y = 216 / 3
y = 72
Hence, when 27 cases of shoes are ordered, the store would order 72 boxes of socks.
3. To determine the personality for the boxes of socks to the cases of shoes, we can express this ratio as a fractional form. From the given information, we know that the ratio between boxes of socks and cases of shoes is 8/3. Therefore, the personality for the boxes of socks to the cases of shoes is 8:3.
4. The constant of proportionality represents the ratio between the two quantities involved. In this case, the constant of proportionality for the cases of shoes to the boxes of socks is the reciprocal of the previous ratio, which is 3/8.