SOLUTION: Debra's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Debra $4.15 per pound, and type B coffee costs $5.70 per pound. This month,

Algebra ->  Linear-equations -> SOLUTION: Debra's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Debra $4.15 per pound, and type B coffee costs $5.70 per pound. This month,       Log On


   



Question 1103656: Debra's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Debra
$4.15
per pound, and type B coffee costs
$5.70
per pound. This month, Debra made
144
pounds of the blend, for a total cost of
$734.00
. How many pounds of type B coffee did she use?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pounds of type A needed
Let +b+ = pounds of type B needed
---------------------------------------
(1) +a+%2B+b+=+144+
(2) +4.15a+%2B+5.7b+=+734+
--------------------------------
(2) +415a+%2B+570b+=+73400+
Multiply both sides of (1) by +415+ and
and subtract (1) from (2)
--------------------------------
(2) +415a+%2B+570b+=+73400+
(1) +-415a+-+415b+=+-59760+
--------------------------------
+155b+=+13640+
+b+=+88+
and
(1) +a+%2B+b+=+144+
(1) +a+%2B+88+=+144+
(1) +a+=+56+
-----------------------
she needs 88 pounds of type B coffee
-----------------------------------
check:
(2) +4.15a+%2B+5.7b+=+734+
(2) +4.15%2A56+%2B+5.7%2A88+=+734+
(2) +232.4+%2B+501.6+=+734+
(2) +734+=+734+
OK