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Question 288280: Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?
{maple syrup: gallons, corn syrup: gallons}
Found 4 solutions by mananth, ikleyn, josgarithmetic, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! Maple syrup worth $6.00 a gallon and corn syrup worth .80 cents a gallon are used to make a mixture worth $2.36 a gallon. How many gallons of each kind of syrup are need to make 50 gallons of the mixture?
{maple syrup: gallons, corn syrup: gallons}
let quantity of maple syrup used be x gallons
corn syrup used will be 50-x gallons
6*x+0,8(50-x)= 2.36*50
6x+40-0.8x=118.00
5.2x=118-40
5,2x=74
x=74/5.2
x=14.2 gallons
35.8 gallons will be corn syrup.
Answer by ikleyn(53765)  (Show Source):
You can put this solution on YOUR website! .
Maple syrup worth $6.00 a gallon and corn syrup worth .80  dollars a gallon
are used to make a mixture worth $2.36 a gallon.
How many gallons of each kind of syrup are need to make 50 gallons of the mixture?
{maple syrup: gallons, corn syrup: gallons}
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There was an obvious typo in the post - I fixed it to make the problem as accurate as it should be.
The solution by @mananth has arithmetic error on the way, which leads to wrong answer.
I came to bring a correct/accurate solution.
let quantity of maple syrup used be x gallons
corn syrup used will be 50-x gallons
6*x + 0.8*(50-x) = 2.36*50
6x + 40 - 0.8x = 118.00
5.2x = 118-40
5.2x = 78
x = 78/5.2
x = 15 gallons of the maple syrup
35 gallons will be the corn syrup.
CHECK for the unit price of the final mixture:  = 2.36 dollars per gallon. ! Precisely correct !
Solved correctly.
Answer by josgarithmetic(39800)  (Show Source):
You can put this solution on YOUR website!
DOLLAR per GAL. GAL. COST, DOLLARS
MAPLE SYR. 6.00 v 6v
CORN SYR. 0.80 50-v 0.8(50-v)
BLENDED 2.36 50 2.36*50
 Solve this for v.
.
Answer by greenestamps(13334)  (Show Source):
You can put this solution on YOUR website!
The responses from the other tutors show setting up and solving the problem using the standard formal algebraic method. That is of course a valid way to solve the problem.
Any 2-part mixture problem like this can also be solved (quickly and easily if the numbers are "nice") using the fact that the ratio in which the two ingredients need to be mixed is exactly determined by where the unit price of the mixture lies between the prices of the two ingredients.
Use a number line if it helps to observe/calculate that 2.36 is 1.56/5.20 = 156/520 = 3/10 of the way from 0.80 to 6.00.
That means 3/10 of the mixture must be the more expensive ingredient.
Since 50 gallons are to be made, the amount of maple syrup needed is (3/10)*50 = 15.
ANSWERS: 15 gallons of maple syrup; 50-15 = 35 gallons of corn syrup
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