Question

alejandro sold apples for $0.50 each and oranges for $0.75 each. he earned a total of $125 from selling these fruits. let $x$ be the number of apples alejandro sold and $y$ be the number of oranges. the system of equations that model this scenario is: $0.50x + 0.75y=125$, $x + y = 200$. how many apples and oranges did alejandro sell? 50 apples and 150 oranges, 150 apples and 50 oranges, 50 apples and 150 oranges, 100 apples and 100 oranges

Explanation:

Step1: Solve the system of equations

We have the system \(

$$\begin{cases}x + y=200\\0.5x + 0.75y=125\end{cases}$$

\). From the first - equation \(x = 200 - y\).

Step2: Substitute \(x\) into the second equation

Substitute \(x = 200 - y\) into \(0.5x+0.75y = 125\), we get \(0.5(200 - y)+0.75y=125\). Expand the left - hand side: \(100-0.5y + 0.75y=125\). Combine like terms: \(100 + 0.25y=125\).

Step3: Solve for \(y\)

Subtract 100 from both sides: \(0.25y=125 - 100=25\). Then \(y=\frac{25}{0.25}=100\).

Step4: Solve for \(x\)

Substitute \(y = 100\) into \(x = 200 - y\), we get \(x=200 - 100 = 100\).

Answer:

100 apples and 100 oranges