Question

Valeria and her children went into a grocery store and she bought $7.50 worth of apples and bananas. Each apple costs $1.50 and each banana costs $0.50. She bought a total of 7 apples and bananas altogether. By following the steps below, determine the number of apples, x, commax, and the number of bananas, y, commay, that Valeria bought.

Answer 1

Valeria bought 4 apples and 3 bananas at the grocery store, by setting up and solving a system of equations representing the total number of fruits and the total cost.

Step-by-step explanation:

To solve the problem of how many apples and bananas Valeria bought given her total spending and the cost of each fruit, we can set up two equations based on the information provided:

1. Let x represent the number of apples, and y represent the number of bananas.
2. The total number of apples and bananas is 7, so we can write the equation x + y = 7.
3. The total cost of apples and bananas is $7.50. Each apple costs $1.50, and each banana costs $0.50. This can be represented by the equation 1.50x + 0.50y = 7.50.
4. To find the value of x and y, we need to solve this system of linear equations.
5. Multiply the second equation by 50 to simplify the coefficients: 150x + 50y = 750.
6. Subtract the first modified equation from the second: (150x + 50y) - (50x + 50y) = 750 - 350, which simplifies to 100x = 400.
7. Divide both sides by 100: x = 4. Valeria bought 4 apples.
8. Substitute x back into the first equation: 4 + y = 7. Thus, y = 3. Valeria bought 3 bananas.

So, Valeria bought 4 apples and 3 bananas at the grocery store.