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?

Answer 1

Answer:

192 pounds of $2.5 brand

288 pounds of $2.8 brand

Step-by-step explanation:

From the information we can write an expression that relates the two brands the total pounds of coffee the grocer wants to see. Let x be pounds of the coffee brand 1 and y be pounds of the coffee brand 2.Equation 1:

$480=x+y$

We know that the price of will be equation 2:

$480*2.68=2.5*x+2.8*y$

Two equations and two unknowns we can solve for x and y:

$x=480-y$

Substitute into the second equation:

$480*2.68=2.5*(480-y)+2.8*y$

$1286.4=1200-2.5*y+2.8*y$

$y=86.4/0.3=288$

Therefore he uses 288 pounds of brand two at $2.80 and 480-288=192 pounds of brand 1 at $2.50

Answer 2

He uses $\boxed{192{\text{ pounds}}}$ of brand 1 at cost $\ 2.50$ and he uses $\boxed{288{\text{ pounds}}}$ of brand 2 at cost $\ 2.80.$

Further explanation:

Given:

The cost of first brand is $\ 2.50.$

The cost of second brand is $\ 2.80.$

Explanation:

The grocer uses a brand of coffee worth $\ 2.50$ a pound with another brand worth $\ 2.80$ a pound.

Let the amount of first brand coffee he blend is $\text{x}$.

Let the amount of second brand coffee he blend is $\text{y}$.

The total amount of coffee is 480 pounds.

$\begin{aligned}x + y &= 480\\ x&= 480 - y\\\end{aligned}$

The price of the blended coffee is $\ 2.68.$

The equation from the price of the coffee can be obtained as follows,

$\begin{aligned}2.5 \times x + 2.8 \times y &= 2.68 \times \left( {x + y} \right)\\2.5x + 2.8y &= 2.68 \times 480\\2.5x + 2.8y &= 1286.4\\\end{aligned}$

Solve the equation to obtain the value of $\text{y}$.

$\begin{aligned}2.5 \times \left( {480 - y} \right) + 2.8y &= 1286.4\\1200 - 2.5y + 2.8y &= 1286.4\\0.3y &= 86.4\\y&= \frac{{86.4}}{{0.3}}\\y&= 288\\\end{aligned}$

The value of $\text{x}$ can be obtained as follows,

$\begin{aligned}x&= 480 - 288\\&= 192\\\end{aligned}$

He uses $\boxed{192{\text{ pounds}}}$ of brand 1 at cost $\ 2.50$ and he uses $\boxed{288{\text{ pounds}}}$ of brand 2 at cost $\ 2.80.$

Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: coffee, grocer, wishes, blend, different, coffee brands, 480 pounds, sell, $2.68, brand worth, brewed, directions, pounds, coffee beans, yields, kilogram, kg, required, produced