Question

Luke and his children went into a grocery store and he bought $9 worth of apples and bananas. each apple costs $1 and each banana costs $0.50. He bought a total of 13 apples and bananas following the steps below, determine the number of apples, x, and the number of bananas, y, that luke bought.

Answer 1

By defining a system of equations based on the cost and quantity of fruits bought by Luke, we solve for x (the number of apples) and y (the number of bananas), resulting in Luke purchasing 5 apples and 8 bananas.

Step-by-step explanation:

The student's question involves solving a system of linear equations to determine the number of apples and bananas Luke bought at a grocery store. We are given the total cost of the fruits and the total number of fruits. We set up our system of equations where x represents the number of apples and y represents the number of bananas. We know each apple costs $1 and each banana costs $0.50.

The two equations that describe this scenario are:

1. x + y = 13 (total number of fruits)
2. $1x + $0.50y = $9 (total cost of fruits)

Multiplying the second equation by 2 to eliminate the fraction, we get 2x + y = 18. Now we subtract the first equation from this new equation to obtain: x = 5. This implies that Luke bought 5 apples. Substituting the value of x into the first equation, we get 5 + y = 13, which gives us y = 8. This means Luke bought 8 bananas.

To summarize, Luke bought 5 apples and 8 bananas.