Together, Levy and Matthew earn $4,680 per month. Levy earns $520 more per month than Matthew earns. How much does Levy earn per month?
A. $2,080
B. $2,340
C. $2,600
D. $4,160
Answer (2)
Define L as Levy's earnings and M as Matthew's earnings.
Write the equations: L + M = 4680 and L = M + 520 .
Substitute the second equation into the first: ( M + 520 ) + M = 4680 , which simplifies to 2 M + 520 = 4680 .
Solve for M and then L: M = 2080 , so L = 2080 + 520 = 2600 . The final answer is $2 , 600 .
Explanation
Problem Analysis Let's analyze the problem. We know that Levy and Matthew together earn $4,680 per month. We also know that Levy earns $520 more than Matthew. Our goal is to find out how much Levy earns per month.
Setting up Equations Let's use variables to represent the unknowns. Let L be the amount Levy earns per month, and let M be the amount Matthew earns per month. We can write two equations based on the given information:
L + M = 4680 (Together, Levy and Matthew earn $4,680)
L = M + 520 (Levy earns $520 more than Matthew)
Substitution Now we can substitute the second equation into the first equation to solve for M:
(M + 520) + M = 4680
Simplifying the Equation Combine like terms:
2M + 520 = 4680
Isolating the Variable Subtract 520 from both sides of the equation:
2M = 4680 - 520
2M = 4160
Solving for Matthew's Earnings Divide both sides by 2 to solve for M:
M = 4160 / 2
M = 2080
So, Matthew earns $2,080 per month.
Solving for Levy's Earnings Now that we know Matthew's earnings, we can find Levy's earnings using the equation L = M + 520:
L = 2080 + 520
L = 2600
Therefore, Levy earns $2,600 per month.
Final Answer The amount Levy earns per month is $2,600.
Examples
Understanding how to solve systems of equations like this is useful in many real-life scenarios. For example, if you're running a business and need to determine the price of two different products, knowing the total revenue and the price difference can help you find the individual prices. Similarly, in personal finance, if you know your total monthly expenses and how much more you spend on one category compared to another, you can calculate the exact amount spent on each category. This type of problem-solving is also applicable in fields like engineering and economics, where you often need to solve for multiple unknowns using related equations.
For instance, imagine a scenario where a store sells apples and bananas. The total revenue from selling apples and bananas is $100. If apples cost $0.50 more than bananas, you can set up a system of equations to find the price of each fruit. Let A be the price of apples and B be the price of bananas. The equations would be:
A + B = 100 (Total revenue)
A = B + 0.50 (Apples cost $0.50 more than bananas)
Solving this system will give you the price of apples and bananas, demonstrating a practical application of solving simultaneous equations.
Levy earns $2,600 per month. This was determined by setting up equations based on their total earnings and the difference in their earnings. By solving these equations, we found Matthew earns $2,080, which allowed us to calculate Levy's earnings.
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