Value Mixture problems

Question

Omar's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Omar
$4.15
per pound, and type B coffee costs
$5.60
per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of
$663.75
. How many pounds of type A coffee were used?

Answer 1

Hi Tyler,

Let X = pounds of type A coffee used

Let Y = pounds of type B coffee used

From the above information, we can write the following equations:

$4.15X + $5.60Y = $663.75

Y = 4X

We can now express the equation in terms of X.

$4.15X + ($5.60)(4X) = $663.75

$4.15X + $22.40X = $663.75

Next, we can solve for X.

4.15X + 22.40X = 663.75

26.55X = 663.75

X = 25

We can now substitute the value of X in equation Y = 4X.

Y = (4)(25)

Y = 100

------------------------------------

$4.15(25) + $5.60(100) = $663.75

$103.75 + $560.00 = $663.75

Twenty-five pounds of Type-A coffee was used.