Question

Earl is ordering supplies. Yellow paper costs $4.00 per ream while white paper costs $7.50 per ream. He would like to order 100 reams total, and has a budget of $484. How many reams of each color should he order?

Answer 1

To solve Earl's problem, set up a system of equations representing the total reams and total cost. Using the elimination method, solve for the number of reams of each color of paper that Earl can order within his budget. Earl should order 76 reams of yellow paper and 24 reams of white paper.

Step-by-step explanation:

The student's question involves solving a system of linear equations and can be approached through a mathematical technique called substitution or elimination. Earl wants to order a total of 100 reams of paper with a budget of $484. Yellow paper costs $4.00 per ream, while white paper costs $7.50 per ream.

Let's denote the number of reams of yellow paper as y and the number of reams of white paper as w. We can then set up our equations based on the given information:

1. Total reams: y + w = 100
2. Total cost: 4y + 7.5w = 484

Using the elimination method, we can multiply the first equation by 4 to give us:

1. 4y + 4w = 400

Subtracting this from the second equation to eliminate y gives:

1. 3.5w = 84

Dividing both sides by 3.5 gives us w = 24, which means Earl can order 24 reams of white paper. Substituting w = 24 into the first equation gives us y = 76. Hence, Earl should order 76 reams of yellow paper and 24 reams of white paper.

Answer 2

Earl should order 76 yellow paper reams and 24 white paper reams.

Step-by-step explanation:

This problem can be computed as system of equations.

I will say that x is the number of yellow paper reams and that y is the number of white paper reams.

Earl will order 100 reams in total, so

x + y = 100

He has a budget of $484, so this is what he is going to spend. Each yellow paper ream(x) costs $4.00 and each white paper ream costs $7.50, so we know that

4x + 7.5y = 484

To know how many reams of each color should he order, we need to solve the following system of equations

1) x + y = 100

2) 4x + 7.5y = 484

I am going to write x as a function of y in equation 1), and then replace it in equation 2).

x = 100-y

Now replacing in equation 2)

4(100-y) + 7.5y = 484

400 - 4y + 7.5y = 484

3.5y = 84

y = 24.

Returning to equation 1)

x = 100-y = 100-24 = 76

So, Earl should order 76 yellow paper reams and 24 white paper reams.