SOLUTION: Hello my dear friends. Learning how to solve word problems is so confusing HELP!!!! 1. In a certain year solar and wind energy generation totaled 1015 trillion BTU'S wind gen

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Question 1012544: Hello my dear friends.
Learning how to solve word problems is so confusing HELP!!!!
1. In a certain year solar and wind energy generation totaled 1015 trillion BTU'S wind generated 52 trillion BTU'S more than 8 times that generated by solar energy. How much was generated by each source.
2. One canned Juice drink is 15% orange juice, another is 5% orange juice. How many liters of each should be mixed together to get 10L that is 6% orange juice.
Thanking you in advance Betty
Found 3 solutions by stanbon, Alan3354, macston:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
In a certain year solar and wind energy generation totaled 1015 trillion BTU'S.
Wind generated 52 trillion BTU'S more than 8 times that generated by solar energy.
Equations:
s + w = 1015 trillion
w = 8s + 52
-----
Substitute for "w" and solve for "s"::
s + 8s+52 = 1015
9s = 963
solar = 107 trillion BTU's
----
Solve for "w"::
w = 8s + 52
wind = 8*107+52 = 908 trillion BTU
------

2. One canned Juice drink is 15% orange juice, another is 5% orange juice. How many liters of each should be mixed together to get 10L that is 6% orange juice.
====
Quantity Eq:: t + f = 10L
OJ Eq:::: 0.15t+0.05f = 0.06*10
---------------------------
Modify for elimination::
15t + 15f = 15*10
15t + 5f = 6*10
----------------
Subtract and solve for "f"::
10f = 9*10
f = 9L (amt. of 5% juice needed)
---
Solve for "t"::
t + f = 10
t + 9 = 10
t = 1L (amt of 15% juice needed)
---------
Cheers,
Stan H.
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Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
1. In a certain year solar and wind energy generation totaled 1015 trillion BTU'S wind generated 52 trillion BTU'S more than 8 times that generated by solar energy. How much was generated by each source.
W = wind amount
S = solar amount
---
W + S = 1015
W = 8S + 52
--
Sub for W
8S+52 + S = 1015
9S = 963
S = 107 Tr
etc
===============================
2. One canned Juice drink is 15% orange juice, another is 5% orange juice. How many liters of each should be mixed together to get 10L that is 6% orange juice.
---
t = 15%
f = 5%
---
t + f = 10 (total solution)
15t + 5f = 10*6 (total OJ)
Solve for t & f

Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website!
.
S=solar; W=wind;
T=trillion (I use this instead of a
fixed value because "trillion" can
mean different things in different in
different countries.)
.
S+W=1015T
W=1015T-S . Use this to substitute for W below.
.
W=8S+52T . Substitute for W from above.
(1015T-S)=8S+52T
963T=9S
107T=S
ANSWER 1: Solar generated 107 trillion BTUs.
.
W=1015T-S=1015T-107T=908T
ANSWER 2: Wind generated 908T BTUs.
.
2)
.
X=amount of 5% juice; Y=amount of 15% juice
.
X+Y=10L
X=10L-Y
.
0.05X+0.15Y=0.06(10L)
0.05(10L-Y)+0.15Y=0.6L
0.5L-0.05Y+0.15Y=0.6L
0.10Y=0.10L
Y=1L
ANSWER 1:Use one liter of 15% juice.
.
X=10L-Y=10L-1L=9L
ANSWER 2: Use nine liters of 5% juice.
.
CHECK:
.
0.05X+0.15Y=0.06(10L)
0.05(9L)+0.15(1L)=0.6L
0.45L+0.15L=0.6L
0.6L=0.6L
.
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