A company produces pens and pencils. If the total production is 500 items and th
Practice Questions
Q1
A company produces pens and pencils. If the total production is 500 items and the number of pens is 4 times the number of pencils, how many pens are produced?
400
100
200
300
Questions & Step-by-Step Solutions
A company produces pens and pencils. If the total production is 500 items and the number of pens is 4 times the number of pencils, how many pens are produced?
Step 1: Let the number of pencils be represented by the variable x.
Step 2: Since the number of pens is 4 times the number of pencils, we can represent the number of pens as 4x.
Step 3: The total production of pens and pencils is given as 500 items. We can write the equation: x (pencils) + 4x (pens) = 500.
Step 4: Combine the terms in the equation: x + 4x = 5x. So, we have 5x = 500.
Step 5: To find the value of x, divide both sides of the equation by 5: x = 500 / 5.
Step 6: Calculate the value: x = 100. This means there are 100 pencils produced.
Step 7: Now, to find the number of pens, use the equation for pens: pens = 4x = 4 * 100.
Step 8: Calculate the number of pens: pens = 400.
Algebraic Equations – The question tests the ability to set up and solve a linear equation based on a word problem.
Proportions – Understanding the relationship between the number of pens and pencils, specifically that the number of pens is four times the number of pencils.
