a college bookstore order six boxes of red pens last week. and 70 red pens this week. 4 pens were left on the shelf. how many pens werein each box?
To find out how many pens were in each box, we need to utilize the information provided and perform some calculations. Let's break it down step by step:
1. Calculate the total number of pens purchased: Last week, the bookstore ordered six boxes of red pens, which we assume to be the same as this week's delivery. Each box contains an unknown number of pens, so we'll call it "x". Therefore, last week's delivery contributed 6 boxes * x pens/box = 6x pens.
2. Add the pens purchased this week: This week, the bookstore purchased 70 pens, which we assume came in the same number of boxes (6 boxes). So, we have an additional 6 boxes * x pens/box = 6x pens from this week's order.
3. Calculate the total number of pens available: Adding up last week's delivery and this week's, we have a total of 6x pens + 6x pens + 70 pens = 12x + 70 pens.
4. Subtract the pens left on the shelf: We are told that 4 pens were left on the shelf. Thus, the total number of pens available is equal to the number of pens left on the shelf plus the pens sold, which gives us 12x + 70 pens - 4 pens = 12x + 66 pens.
5. Set up the equation: We know that the total number of pens available is equal to 12x + 66 pens. This should be equal to the total number of pens purchased so far, which is 6x + 70 pens. Therefore, we have the equation: 12x + 66 = 6x + 70.
6. Solve the equation: To solve for x, we need to isolate it on one side of the equation. First, let's subtract 6x from both sides: 12x - 6x + 66 = 6x - 6x + 70, which simplifies to 6x + 66 = 70.
7. Continue solving the equation: Next, let's subtract 66 from both sides: 6x + 66 - 66 = 70 - 66, which simplifies to 6x = 4.
8. Find the value of x: To find the value of x, we'll divide both sides of the equation by 6: 6x/6 = 4/6, which simplifies to x = 2/3.
Therefore, each box contained 2/3 (or 0.67) pens.