Ran had some boxes of biscuits for sale. He sold 140 boxes on Friday. He sold 1/4 of the remaining boxes of biscuits on Saturday. Then he had 2/5 of the total number of boxes of biscuits left, how many boxes of biscuits did he have at first?
The name is supposed to be Raj not Ran
300
To determine how many boxes of biscuits Raj initially had, let's go backwards.
Raj still had two-fifths of the total number of biscuit boxes after Saturday's sales. This indicates that before Saturday's sales, he still owned 3/5 of the boxes.
Let's refer to Raj's initial stock of biscuits boxes as having "x" totals. He has x–140 boxes left after selling 140 boxes on Friday. Later, on Saturday, he sold one-fourth of the unsold boxes. This indicates that on Saturday, he sold (1/4)(x - 140) boxes. As a result, following Saturday's sales, he still owned 3/4 of the remaining boxes.
For this, we may construct an equation as follows:
3/4(x - 140) = 2/5x
To eliminate the fractions, multiply both sides by 20 (the least common multiple of 4 and 5), and the result is:
15(x - 140) = 8x
Increasing the brackets results in:
15x - 2100 = 8x
8x is subtracted from both sides to yield:
7x - 2100 = 0
2100 added to both sides gives us:
7x = 2100
When we multiply both sides by 7, we get:
x = 300
Raj therefore started out with 300 boxes of biscuits.
To solve this problem, we can work backwards from the information given. Let's break down the steps:
Step 1: Number of boxes sold on Friday
Ran sold 140 boxes of biscuits on Friday, which means that the number of boxes remaining after Friday is the total number of boxes minus 140.
Step 2: Number of boxes sold on Saturday
Ran sold 1/4 of the remaining boxes of biscuits on Saturday. Since 1/4 is equivalent to 2/8, we can say that 2/8 of the remaining boxes were sold on Saturday. This means that 6/8 (or 3/4) of the remaining boxes of biscuits were left.
Step 3: Number of boxes remaining
The problem states that Ran had 2/5 of the total number of boxes of biscuits left after Saturday. Since 2/5 of the total is equivalent to 8/20, we can say that 8/20 of the total number of boxes were left at this point.
Step 4: Calculate the initial number of boxes
To find the initial number of boxes, we need to work backwards from the information we have. We can set up an equation and solve for the unknown initial number of boxes, represented as "x":
x - 140 = (3/4)x - (8/20)x
Simplifying the equation:
(3/4)x - (8/20)x = x - 140
(15/20)x - (8/20)x = x - 140
(7/20)x = x - 140
7x = 20x - 2800
-13x = -2800
x = (-2800)/(-13)
x ≈ 215.38
Therefore, the initial number of boxes Ran had was approximately 215.