Mathematics, 01.08.2019 11:30 oasmith2005

Agrocer 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?

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Answer from: jessecabrown1

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 from: hmjjones

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:

Learn more about inverse of the function . Learn more about equation of circle . Learn more about range and domain of the function

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

Answer from: Quest

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is $3\times 8.50=$25.5$