Solving Real-Life Mysteries with Simultaneous Equations: An SEO Optimized Guide
Do you ever encounter situations where you need to figure out the cost of items based on given conditions? In this article, we’ll walk through a real-life example and demonstrate how to solve these puzzling problems using simultaneous equations. This not only helps in understanding but also ensures content that’s highly SEO-friendly for search engines like Google. Let’s dive in!
A Recap: Using Equations to Crack Puzzles
Imagine a group of friends meeting for lunch. During their meal, they struggle to figure out the prices of their favorite hot dogs and cheeseburgers. They have two scenarios:
The first order consists of 2 hot dogs and 4 cheeseburgers, costing a total of 23.50. The second order includes 5 hot dogs and 1 cheeseburger, totaling 18.25.We can use simultaneous equations to solve this puzzle. Let’s denote:
h as the cost of a hot dog. c as the cost of a cheeseburger.By setting up equations based on the given information, we can find the cost of a hot dog.
Setting Up the Equations
Based on the given information, we can set up the following equations:
2h 4c 23.50 (Equation 1)
5h 1c 18.25 (Equation 2)
Let’s solve these equations step by step:
Step 1: Simplify Equation 1
Divide Equation 1 by 2:
h 2c 11.75 (Equation 3)
Step 2: Solve for c in terms of h
From Equation 3, we can express c in terms of h:
2c 11.75 - h
c (11.75 - h) / 2 (Equation 4)
Step 3: Substitute Equation 4 into Equation 2
Now, substitute Equation 4 into Equation 2:
5h (11.75 - h) / 2 18.25
Multiplying the entire equation by 2 to eliminate the fraction:
10h 11.75 - h 36.50
9h 11.75 36.50
Step 4: Solve for h
Isolate h:
9h 36.50 - 11.75
9h 24.75
h 24.75 / 9 2.75
Therefore, the cost of a hot dog is 2.75.
Imaginary Scenario for Additional Practice
For fun, let’s imagine a different scenario:
Two friends have hamburgers, and five have hot dogs, costing a total of 8.00. Five friends have hamburgers, and two have hot dogs, costing 9.50.Let’s denote:
H as the price of a hamburger. D as the price of a hot dog.The equations are:
2H 5D 8.00 (a)
5H 2D 9.50 (b)
Solving the Equations
Eliminate D by multiplying (a) by 2 and (b) by 5:
4H 10D 16.00 (iii)
25H 10D 47.50 (iv)
Subtract (iii) from (iv):
21H 31.50
H 31.50 / 21 1.50
A hamburger costs 1.50.
Final Question
A group of students go out for lunch. If two have hamburgers and five have hot dogs the bill will be 8.00. If five have hamburgers and two have hot dogs the bill will be 9.50. What is the price of a hamburger?
Let’s denote:
H as the price of a hamburger. D as the price of a hot dog.Hence from the given data:
2H 5D 8.00 (a)
5H 2D 9.50 (b)
Therefore, from 5b - 2a, we get:
21H 31.50
H 31.50 / 21 1.50
The price of a hamburger is 1.50.
Conclusion
Using simultaneous equations, we can solve real-life mysteries and ensure that our content is SEO-optimized for search engines. Whether it’s finding the cost of a hot dog or a hamburger, understanding these methods makes problem-solving much more manageable.