Question

Help please
Mai's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Mai
$4.45
per pound, and type B coffee costs
$5.95
per pound. This month, Mai made 149
pounds of the blend, for a total cost of $798.05
. How many pounds of type A coffee did she use?

Answer 1

Since there are two types of coffees, we'll label:

Type A = x, Type B = y

Answer 2

We're given that altogether, Mai made 149 lbs of the blend, this means that our first equation can be written as:

x + y = 149

Answer 3

Now, we can derive another equation from this problem concerning the cost of each of these types of coffees.

x = $4.45 and y = $5.59

Together these two add to a total of $798.05

Therefore our equation becomes :

4.45x + 5.59y = 798.05

Answer 4

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Answer 5

Now that we've got our two equations:

x + y = 149

4.45x + 5.59y = 798.05

We can solve for both types of coffee.

There are two methods to solving these equations: substitution and elimination.

Let's try elimination.

Answer 6

I realized multiplying by -5.59 will give us a negative value and it will result in a negative amount of money, which is not possible.

Answer 7

So let's try eliminating the x first.

-4.45( x+ y = 149)
4.45 + 5.59y = 798.05
___________________________

0 + (5.59y - 4.45y) = 798.05 - 663.05

Answer 8

1.14y = 135

y = \(\ \large \frac{135}{1.14}\)
y = 118.421

Answer 9

Plugging the y value into our first equation, we can solve for x, or the "Type A" coffee used.

x + 118.421 = 149
x = 149 - 118.421
x = 30.579
x = 31 lbs of coffee