SOLUTION: One unit of whole wheat flour has 13.6 grams of protein and 2.5 grams of fat. One unit of whole milk has 3.4 grams of protein and 3.7 grams of fat. To the nearest tenth fin dthe nu

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: One unit of whole wheat flour has 13.6 grams of protein and 2.5 grams of fat. One unit of whole milk has 3.4 grams of protein and 3.7 grams of fat. To the nearest tenth fin dthe nu      Log On


   



Question 609323: One unit of whole wheat flour has 13.6 grams of protein and 2.5 grams of fat. One unit of whole milk has 3.4 grams of protein and 3.7 grams of fat. To the nearest tenth fin dthe number of units of whole wheat flour and whole milk that must be mixed to make dough that has 75 grams of protein and 15 grams of fat.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = units of whole wheat flour needed
Let +b+ = units of whole milk needed
given:
+a+ units of whole wheat flour has +13.6a+ grams protein
+a+ units of whole wheat flour has +2.5a+ grams fat
+b+ units of whole milk has +3.4b+ grams protein
+b+ units of whole milk has +3.7b+ grams fat
-----------------
(1) +13.6a+%2B+3.4b+=+75+
(2) +2.5a+%2B+3.7b+=+15+
---------------------
(1) +136a+%2B+34b+=+750+
(2) +25a+%2B+37b+=+150+
----------------------
Multiply both sides of (2) by +34%2F37+
(2) +25%2A%2834%2F37%29a+%2B+34b+=+%2834%2F37%29%2A150+
(2) +22.973a+%2B+34b+=+137.838+
Subtract (2) from (1)
(1) +136a+%2B+34b+=+750+
(2) +-22.973a+-+34b+=+-137.838+
+113.027a+=+612.162+
+a+=+5.416+ units
and, since
(2) +25a+%2B+37b+=+150+
(2) +25%2A5.416+%2B+37b+=+150+
(2) +135.4+%2B+37b+=+150+
(2) +37b+=+150+-+135.4+
(2) +37b+=+14.6+
(2) +b+=+.395+
5.4 units of whole wheat flour is needed
.4 units of whole milk are needed
check:
(1) +13.6%2A5.4+%2B+3.4%2A.4+=+75+
(1) +73.44+%2B+1.36+=+75+
(1) +74.8+=+75+ ( close )
(2) +2.5%2A5.4+%2B+3.7%2A.4+=+15+
(2) +13.5+%2B+1.48+=+15+
(2) +14.98+=+15+
OK