Coffee For Two

How would I solve this mixture word problem: Suppose that you want to blend two coffees in order to obtain a?

new blend. The blend will be made with the best Arabica beans that sell for $9.00 per pound and select African Robustas that sell for $11.50 per pound to obtain 100 pounds of the new blend. The new blend will sell for $10.00 per pound and there will be no difference in revenue from selling the new blend versus selling the beans seperately. How many pounds of the Arabica and Robusta beans are required?

this will be a simultaneous equation problem or matrix problem

take X to be amount in lbs of Arabica beans
take Y to be amount in lbs of African robustas..

set up two equations one for cost

9*X + 11.50*Y = 10.

that means some of X at 9 dollars plus some of Y at 11.50 will add to 10 dollars even

we also know the total weight is 100 lbs

X + Y = 1

now this is the kinda tricky part I set up the weight to be X + Y = 1 lb because the above equation before was for the price of 1 LB of coffee..

now solve the two equations

we can do this easy by solving for Y in the second equation..

Y = 1 – X
now put this in the other equation we had
9*X + 11.50*Y = 10.

this becomes
9*X + 11.5*(1-X) = 10

solve for X

9X + 11.5 -11.5X = 10
-2.5X = -1.5
X = -1.5/(-2.5)
X = 0.6 lbs of Arabica beans in 1 lb of blend
we know this so
Y = 1 – X
Y = 1 – 0.6 = 0.4

so 0.4 lbs of African Robustas in the 1 lb blend

that means for 100lbs we need to times each amount by 100

0.6 *100 = 60lbs of Arbaica
and
0.4*100 = 40lbs of African Robustas

thats the answer..

you can chck this by putting the 0.6 and 0.4 in the top equation to see if it comes to 10 on the left side

Krups 203 Electric Coffee and Spice Grinder with Stainless-Steel Blades …

Keurig B60 Special Edition Gourmet Single-Cup Home-Brewing System …

Cuisinart DCC-RWF1 Replacement Coffeemaker Water Filters, Set of 2 $3.50 Cuisinart DCC-RWF Coffee Water Filter Replacement…

Ladies of the Canyon $4.11 Joni Mitchell’s third album offers a bridge between the artful but sometimes dour meditations of her earlier work and the more mature, confessional revelations of the classics that would follow. Voice and guitar still hew to the pretty filigree of a folk poet, but there’s the giggling rush of rock & roll freedom in “Big Yellow Taxi,” and the formal metaphor of her older songs (“The Circle Game,” a…

Sign O the Times $6.27 ************CHECK OUT MY MANY RARE AND HARD TO FIND JAZZ ,ROCK & FUNK , CDS FEATURE IN MY STORE ************* PLEASE NOTICE THAT EACH AND EVERY BOX SET HAS BEEN PERSONALLY INSPECTED TO INSURE QUALITY AND ACCURATE DESCIPTIONS THERE ARE NO RETURNS ON OPEN BOX SETS***************…

Desire (Reis) $4.49 All products are BRAND NEW and factory sealed. Fast shipping and 100% Satisfaction Guaranteed….

Bull Riders Only: Best Rides & Best Wrecks 2 [VHS] $9.98 …

Belkin Mini Surge Protector Dual USB Charger $13.30 Protect your electronic devices while traveling….

Belkin Conserve Socket F7C009q Energy-Saving Outlet $9.66 Conserve Socket Power Timer. Many of the electronics and appliances around your home use electricity even when they’re not in use wasting energy and driving up your electric bill. The Conserve Socket Power Timer automatically shuts off power (including standby power) to your electronics and appliances after a time interval you select to help you save energy. Choose between three settings: 30 minut…

Belkin Conserve Socket with Energy-Saving Outlet $24.98 Conserve Smart AV Auto-Off Surge Protector. Now you can automatically turn off up to five entertainment system ponents when you turn off your TV and easily reduce standby power. The Master Outlet senses when your TV is on or off and controls power to five peripheral outlets for your AV ponents. Two outlets stay on for devices that need continuous power like DVRs. Control power to your whole entert…