Fuj apples cost $3.00 per pound and Given Detros apples cost $2.00 per pound. A purchaser purchases 30 pounds of a combination of the two types of apples for a total of $80.
Answer (1)
Achibratereta purchased 20 pounds of Fuj apples and 10 pounds of Detros apples.
Explanation
Problem Analysis We are given that Fuj apples cost $3.00 per pound and Detros apples cost $2.00 per pound. Achibratereta purchases a total of 30 pounds of apples for a total cost of $80. We want to determine how many pounds of each type of apple were purchased.
Setting up the Equations Let x be the number of pounds of Fuj apples purchased and y be the number of pounds of Detros apples purchased. We can set up a system of two equations with two variables:
The total weight of the apples is 30 pounds: x + y = 30
The total cost of the apples is $80: 3 x + 2 y = 80
Solving for x We can solve this system of equations using substitution or elimination. Let's use substitution. From the first equation, we can express y in terms of x : y = 30 − x . Now, substitute this expression for y into the second equation:
3 x + 2 ( 30 − x ) = 80
Simplify and solve for x :
3 x + 60 − 2 x = 80
x = 80 − 60
x = 20
Solving for y Now that we have the value of x , we can find the value of y :
y = 30 − x = 30 − 20 = 10
Final Answer So, Achibratereta purchased 20 pounds of Fuj apples and 10 pounds of Detros apples.
Examples
Understanding systems of equations is crucial in various real-life scenarios. For instance, consider a situation where you're managing a budget and need to allocate funds between two different investment options with varying returns. By setting up a system of equations, you can determine the optimal amount to invest in each option to maximize your overall return while staying within your budget constraints. This approach is also applicable in fields like chemistry, where you might need to balance chemical equations, or in economics, where you could analyze supply and demand curves to find equilibrium prices and quantities.
