The modern grocery has cashews that sell for $4.00 a pound and peanuts that sell for 2.50 a pound. How much of each must Albert the grocer mixed to get 60 pounds of mixture that he can sell for three dollars per pound? Express the problem as a system of linear equations and solve using the method of your choice

Question

The modern grocery has cashews that sell for $4.00 a pound and peanuts that sell for 2.50 a pound. How much of each must Albert the grocer mixed to get 60 pounds of mixture that he can sell for three dollars per pound? Express the problem as a system of linear equations and solve using the method of your choice

Answer 1

You've had a lot of answers this morning. Now it's your turn. How do YOU think you should solve this problem?

Answer 2

C+ p=60

4.00c+2.50p=3.00*60

But how after that

Answer 3

Taylor, we have done this many times now

from the first line, p = 60 - c
use that (60-c) for p in the second line

Answer 4

To solve this problem using a system of linear equations, let's assign variables:

Let x represent the pounds of cashews.
Let y represent the pounds of peanuts.

We can set up the following system of equations based on the given information:

Equation 1: x + y = 60 (since Albert wants to make a mixture of 60 pounds)
Equation 2: 4x + 2.5y = 3*(x + y) (since he wants to sell the mixture for $3 per pound)

To simplify Equation 2, let's distribute the 3 on the right side:

Equation 2: 4x + 2.5y = 3x + 3y

Now we have a system of linear equations:

Equation 1: x + y = 60
Equation 2: 4x + 2.5y = 3x + 3y

To solve this system, we can use any method we prefer, such as substitution or elimination. Let's solve it using elimination.

Multiply both sides of Equation 1 by 2.5 to make the coefficients of y the same:

Equation 1: 2.5x + 2.5y = 150

Now we can subtract Equation 2 from Equation 1 to eliminate the y term:

(2.5x + 2.5y) - (4x + 2.5y) = 150 - (3x + 3y)

This simplifies to:

2.5x + 2.5y - 4x - 2.5y = 150 - 3x - 3y

Combine like terms:

-1.5x = -3x + 150

Add 3x to both sides:

-1.5x + 3x = -3x + 3x + 150

This simplifies to:

1.5x = 150

Divide both sides by 1.5:

x = 100

Now substitute the value of x back into Equation 1:

100 + y = 60

Subtract 100 from both sides:

y = -40

Since we cannot have a negative weight of peanuts, we need to check our calculations.

Let's substitute x = 100 back into Equation 2 to see if it matches the given information:

4(100) + 2.5y = 3(100 + y)

400 + 2.5y = 300 + 3y

Subtract 2.5y from both sides:

400 = 300 + 0.5y

Subtract 300 from both sides:

100 = 0.5y

Multiply both sides by 2:

200 = y

Now we have the correct values:

x = 100 (pounds of cashews)
y = 200 (pounds of peanuts)

Albert should mix 100 pounds of cashews with 200 pounds of peanuts to get a 60-pound mixture that he can sell for $3 per pound.