Write a math word problem about Dic having pencils using this expression
2/4x + 12/24x + 2x + 4 = 7
Dic has a total of x pencils. If he uses 2/4 of his pencils to color his drawings and 12/24 of his pencils to write notes, he will have 2x pencils left. If Dic finds 4 more pencils, he will have a total of 7 pencils. How many pencils did Dic have at the beginning?
Sure! Here's a math word problem involving Dic and his pencils:
Dic has a collection of pencils. He decides to organize them into groups based on their lengths. He starts by grouping them into three categories: short pencils, medium pencils, and long pencils.
Dic knows that the total number of pencils in each category can be represented by the expression:
(2/4x) + (12/24x) + 2x + 4 = 7
To solve this problem, we can follow these steps:
Step 1: Simplify the expression
2/4x can be simplified to 1/2x, and 12/24x can be simplified to 1/2x as well. So, the expression becomes:
1/2x + 1/2x + 2x + 4 = 7
Step 2: Combine like terms
The two terms 1/2x can be combined as 1x or x. So, the expression becomes:
x + x + 2x + 4 = 7
4x + 4 = 7
Step 3: Solve for x
To isolate the variable x, we need to subtract 4 from both sides of the equation:
4x + 4 - 4 = 7 - 4
4x = 3
Finally, divide both sides of the equation by 4 to solve for x:
4x/4 = 3/4
x = 3/4
So, the solution to the problem is x = 3/4. This means that Dic has 3/4 as many pencils as the total number of pencils in his groups.