Show a complete solution to each problem. Blending coffee....

Show a complete solution to each problem. Blending coffee. Mark blends $\frac{3}{4}$ of a pound of premium Brazilian coffee with $1 \frac{1}{2}$ pounds of standard Colombian coffee. If the Brazilian coffee sells for $\$ 10$ per pound and the Colombian coffee sells for $\$ 8$ per pound, then what should the price per pound be for the blended coffee?

Show a complete solution to each problem.
Blending coffee. Mark blends $\frac{3}{4}$ of a pound of premium Brazilian coffee with $1 \frac{1}{2}$ pounds of standard Colombian coffee. If the Brazilian coffee sells for $\$ 10$ per pound and the Colombian coffee sells for $\$ 8$ per pound, then what should the price per pound be for the blended coffee?

Key Concepts

Fraction Arithmetic

Fraction arithmetic includes operations such as addition, subtraction, multiplication, and division applied to fractions. Mastery of these skills is essential for manipulating fractional values accurately, as many real-world problems involve quantities and measurements expressed in fractions.

Unit Price Calculation

Unit price calculation is the process of determining the cost or value of a single unit by dividing the total cost by the total number of units. This method is fundamental in comparing prices, conducting cost analyses, and ensuring that pricing is set appropriately in situations where individual unit values are derived from combined masses or quantities.

Weighted Average

Weighted average is a method for finding the overall average when different components contribute unequally to the total. It is especially useful for blending or mixing scenarios where each component has its own price or value and quantity, and the final average is calculated by considering the proportional influence of each component.

Conversion of Mixed Numbers to Improper Fractions

This concept involves rewriting mixed numbers as improper fractions to simplify arithmetic operations. Converting mixed numbers to a consistent fraction format helps in performing multiplication, addition, or division with greater ease, which is particularly useful in solving problems involving fractional quantities.

Transcript

00:01 In this problem, we have a man that makes us three -fourths of a pound of coffee type a with one and a half pounds of coffee type b.

00:10 And coffee type a costs $10 per pound, and coffee b costs $8 per pound.

00:16 We want to know what should he charge per pound for his mix, and we need to show the complete solution.

00:24 So let's go ahead and start by figuring out what this total mix is going to cost.

00:31 Cost him.

00:32 So we know that coffee type a costs $10 per pound and he used three -fourths of a pound.

00:41 So if we take $10 multiplied by our three -fourths, that should give us our total cost of coffee type a.

00:52 Okay, so now we need to deal with coffee type b.

00:56 So if we add the cost of coffee type b, which he used one and a half pounds, and it costs $8 per pound.

01:09 So if we multiply those two numbers, that'll give us the total for coffee type b.

01:15 So let's go ahead and do this problem and figure out how much this mix cost him total when all is said and done.

01:26 So let's go ahead and take 10 multiplied by a three -fourths, and that's going to give me 7.

01:35 And a half.

01:38 Or in this case, let's do it in decimals, so we can have a nice number value.

01:46 So in this case, it would be $7 .5 or $7 .50 plus $8 times one and a half or 1 .5 pounds.

02:00 That's going to give us a nice round number of $12.

02:05 So we have $12 plus $7 .50 is going to give us a total of $19 .50.

02:16 Okay, so that's the total cost of our mix.

02:19 But now we need to figure out how much he should charge per pound.

02:24 Well, let's also figure out how many total pounds went into this mix.

02:31 So i'm going to label this so we can keep it straight here...

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