Question

Melons cost $20 per crate, and apples cost $8 per crate. A total of 48 crates are purchased for $420. Determine the number of crates of melons and apples.

Answer 1

There are 3 crates of melons and 45 crates of apples.

Step-by-step explanation:

Let's assume the number of crates of melons to be 'x' and the number of crates of apples to be 'y'.

According to the given information, each crate of melons costs $20 and each crate of apples costs $8.

Using this information, we can form the following equations:

x + y = 48 (equation 1) --> because the total number of crates purchased is 48

20x + 8y = 420 (equation 2) --> because the total cost of the crates is $420

To solve this system of equations, we can use the substitution method or the elimination method.

Let's use the elimination method:

Multiplying equation 1 by 8, we get:

8x + 8y = 384 (equation 3)

Subtracting equation 3 from equation 2, we get:

(20x + 8y) - (8x + 8y) = 420 - 384

12x = 36

Dividing both sides of the equation by 12, we get:

x = 3

Substituting the value of x into equation 1, we get:

3 + y = 48

y = 45

Therefore, there are 3 crates of melons and 45 crates of apples.