A salesperson bought a caase of pens.On Monday, he sold 1/2 of the pens.On Tuesady, he sold 30 more.On Wednesday, he sold 1/3 of the pens that were left.On Thursday, he sold the remaining 40 pens.How many pens were originally in the case,
96
96 is a nice number, but it is not the answer to your problem.
Let x = total number of pens
.5x = Monday sales, which means that .5x remain.
30 = Tuesday sales
1/3(.5x-30) = Wednesday sales
40 remained on Thursday
.5x - 30 - 1/3 (.5x -30) = 40
Solve for x.
I hope this helps. Thanks for asking.
Let's break down the information given step-by-step to find out how many pens were originally in the case:
1. On Monday, the salesperson sold 1/2 of the pens.
Let's say he sold "x" pens on Monday. So he had "x" pens left.
2. On Tuesday, he sold 30 more pens.
After selling 30 more pens, he had "x - 30" pens left.
3. On Wednesday, he sold 1/3 of the remaining pens.
Let's calculate: (1/3) * (x - 30) = (x - 30)/3
So, he sold (x - 30)/3 pens on Wednesday.
After this sale, he had (x - 30) - (x - 30)/3 pens left.
4. On Thursday, he sold the remaining 40 pens.
After selling the remaining pens, he had 0 pens left.
Now we can set up an equation to solve for the original number of pens:
x - 30 - (x - 30)/3 = 40
To simplify this equation, let's multiply everything by 3:
3(x - 30) - x + 30 = 120
3x - 90 - x + 30 = 120
2x - 60 = 120
Add 60 to both sides of the equation:
2x = 180
Divide both sides by 2:
x = 90
Therefore, the original number of pens in the case was 90.
To find the number of pens originally in the case, let's work through the problem step by step.
Step 1: On Monday, the salesperson sold 1/2 of the pens. Let's represent the original number of pens as 'x'. So, on Monday, the salesperson sold x/2 pens, which means he has x - (x/2) pens left.
Step 2: On Tuesday, the salesperson sold 30 more pens. So, the number of pens remaining after Tuesday's sale is (x - (x/2)) - 30.
Step 3: On Wednesday, he sold 1/3 of the pens that were left. Therefore, he sold (1/3) * ((x - (x/2)) - 30) pens on Wednesday, leaving us with (x - (x/2)) - 30 - ((1/3) * ((x - (x/2)) - 30)) pens.
Step 4: On Thursday, he sold the remaining 40 pens. So, the number of pens left after Thursday's sale is ((x - (x/2)) - 30 - ((1/3) * ((x - (x/2)) - 30))) - 40.
We know that this number is equal to 0 since there are no pens left after Thursday's sale. Therefore, we can solve the equation:
((x - (x/2)) - 30 - ((1/3) * ((x - (x/2)) - 30))) - 40 = 0
By simplifying and solving this equation, we can find the value of x, which represents the number of pens originally in the case.