A store has a total of 1,957 CD's. The number of hip-hop CD's is 256 fewer than the number of pop CD's. There are three times as many hip-hop CD's as country CD's.
a. draw bar models to represent the amount of each of the three types of CD's.
b. write the expression you used to determine the value of a unit in your bar model.
c. if all of the country CD's were placed into three boxes, how many CD's would there be in each box?
a. 1957 total CDs.
X pop CDs.
x-256 hip-hop CDs.
(x-256)/3 country CDs.
x + (x-256) + (x-256)/3 = 1957.
Multiply both sides by 3 and solve for x.
c. Country CDs/3.
a. To represent the amount of each type of CD, we can use bar models. Let's start with the total number of CDs, which is 1,957. We can divide this bar into three parts to represent the three types of CDs: pop, hip-hop, and country.
Let's say the length of the pop CD bar is x. Then the length of the hip-hop CD bar would be x - 256 (since the number of hip-hop CDs is 256 fewer than the number of pop CDs). The length of the country CD bar would be 1/3 of the length of the hip-hop CD bar, which is (1/3)*(x - 256).
The bar model representation would look like this:
Total CDs: ------------[x]----------------
Pop CDs: ------[x]---------------------
Hip-hop CDs: ---[x - 256]---------------
Country CDs: ----[1/3*(x - 256)]-------
b. To find the expression for the value of a unit in the bar model, we need to determine the value of x. We know that the total number of CDs is 1,957, so we can express this as an equation:
x + (x - 256) + 1/3*(x - 256) = 1,957.
Simplifying the equation, we get:
x + x - 256 + 1/3*x - 256/3 = 1,957.
Combining the like terms and simplifying further, we get:
11/3*x = 3,425.
To solve for x, we multiply both sides of the equation by 3/11:
x = (3,425 * 3) / 11 = 935.
So, the expression for the value of a unit in the bar model is x = 935.
c. If all the country CDs were placed into three boxes, we need to find the number of CDs in each box. From the bar model, we know that the length of the country CD bar is 1/3*(x - 256). Substituting the value of x we found earlier:
Number of CDs in each box = 1/3*(935 - 256) = 1/3*(679) = 226.
Therefore, there would be 226 country CDs in each of the three boxes.