Question

Pears cost $2 each. Melons cost $3 each. Elijah bought a total of 8 pears and melons, and spent $19. How many pears and how many melons did Elijah buy?

Answer 1

To determine the number of pears and melons Elijah bought, we create a system of equations based on the total number and cost of the fruits. By solving the equations, we find that Elijah bought 5 pears and 3 melons.

Step-by-step explanation:

To solve the problem of determining how many pears and melons Elijah bought, we can use a system of equations based on the given information. Let's define p as the number of pears and m as the number of melons. We have two pieces of information that will translate into two equations:

1. The total number of fruits is 8, so p + m = 8.
2. The total amount spent is $19, so 2p + 3m = 19 (since pears cost $2 each and melons cost $3 each).

Now, we will solve the system of equations step-by-step:

1. First, we express m in terms of p from the first equation: m = 8 - p.
2. Next, we substitute m in the second equation: 2p + 3(8 - p) = 19.
3. Simplifying, we get: 2p + 24 - 3p = 19.
4. Combining like terms gives us: -p = -5.
5. Therefore, p = 5, meaning Elijah bought 5 pears.
6. To find the number of melons, we substitute p back into the equation for m: m = 8 - 5 = 3.

Elijah bought 5 pears and 3 melons.