A grocer wishes to blend two different coffee brands because he wants to make a blend of 480 pounds to sell at $2.68 a pound. If he uses a brand of coffee worth $2.50 a pound with another brand worth $2.80 a pound, how many pounds of each does he use?

Question

A grocer wishes to blend two different coffee brands because he wants to make a blend of 480 pounds to sell at $2.68 a pound. If he uses a brand of coffee worth $2.50 a pound with another brand worth $2.80 a pound, how many pounds of each does he use?

Please tell me the steps to solve this

Answer 1

done here

http://www.jiskha.com/display.cgi?id=1438656557

Answer 2

2.5x + 2.8(480-x) = 2.68(480)

2.5x + 1344 - 2.8x = 128.40
-.3x = -57.6
x = 192

Answer 3

To solve this problem, you can set up a system of equations by assigning variables to the unknown quantities. Let's say the number of pounds of coffee from the first brand is represented by x, and the number of pounds from the second brand is represented by y.

We are given that the grocer wants to make a blend of 480 pounds of coffee. So the first equation would be:

x + y = 480

Next, we know that the price of the first brand of coffee is $2.50 per pound, and the price of the second brand is $2.80 per pound. We want to sell the blend at $2.68 per pound. To determine the second equation, we need to consider the total value of the blend. The total value of the coffee can be found by multiplying the amount of each brand by its respective price and then adding them together:

(2.50 * x) + (2.80 * y) = (2.68 * 480)

Simplifying the above equation, we have:

2.50x + 2.80y = 1286.40

Now you have a system of two equations:

x + y = 480
2.50x + 2.80y = 1286.40

You can solve this system of equations using various methods, such as substitution, elimination, or graphing. Let's solve it using the substitution method.

From the first equation, we can rewrite it as:

x = 480 - y

Substituting this equation into the second equation:

2.50(480 - y) + 2.80y = 1286.40

Simplify the equation:

1200 - 2.50y + 2.80y = 1286.40
0.30y = 86.40
y = 86.40 / 0.30
y ≈ 288

Now that we have the value of y, we can substitute it back into either equation to find x. Let's use the first equation:

x + y = 480
x + 288 = 480
x = 480 - 288
x = 192

Therefore, the grocer should use 192 pounds of the first coffee brand and 288 pounds of the second coffee brand to make a blend of 480 pounds to sell at $2.68 per pound.

Answer 4

2.5x + 2.8(480-x) = 2.68(480)

2.5x + 1344 - 2.8x = 128.40
-.3x = -57.6
x = 192

so he should use 192 pounds of the $2.50 and
288 pounds of the $2.80 stuff

check:
cost of the parts = 2.5(192) + 2.8(288) = 1286.40
cost of the mix = 2.68(480) = 1286.40