A restaurant has one type of lemonade that is 12% sugar and another that is 7% sugar. How many gallons of each type does the restaurant need to make 20 gallons of a lemonade mixture that is 10% sugar?

A) 12 gallons of the 12% lemonade and 8 gallons of the 7% lemonade
B) 10 gallons of the 12% lemonade and 10 gallons of the 7% lemonade
C) 8 gallons of the 12% lemonade and 12 gallons of the 7% lemonade
D) 2 gallons of the 12% lemonade and 18 gallons of the 7% lemonade

Question

A restaurant has one type of lemonade that is 12% sugar and another that is 7% sugar. How many gallons of each type does the restaurant need to make 20 gallons of a lemonade mixture that is 10% sugar? 

A) 12 gallons of the 12% lemonade and 8 gallons of the 7% lemonade
B) 10 gallons of the 12% lemonade and 10 gallons of the 7% lemonade
C) 8 gallons of the 12% lemonade and 12 gallons of the 7% lemonade
D) 2 gallons of the 12% lemonade and 18 gallons of the 7% lemonade

anonymous · Answer

no idea

anonymous · Answer

@Luigi0210 can you help me please? (:

anonymous · Answer

@hartnn I need help once again lol

luigi0210 · Answer

I kind of have to leave soon, but I think hartnn can figure it out c:

anonymous · Answer

okay!

hartnn · Answer

let
x be the number of gallons of 12% sugar lemonade
y = number of gallons of 7% sugar lemonade
since we need 20 gallons of a lemonade mixture that is 10% sugar,
we first have x+y =20
got this ?

anonymous · Answer

so x + y = 20
12 + 7

anonymous · Answer

nevermind 12 and 7 are the percentages not gallons

hartnn · Answer

ok, we need one more equation,
12% of sugar x = 0.12 x
7% of sugar y = 0.07y
this should equal, 10% of sugar in 20 gallons mixture which is 0.10*20 

so we have 
0.12x+0.07y = 0.10*20
see if u get this...

anonymous · Answer

yes I get it

hartnn · Answer

now you have 2 equations, 2 unknowns, can you solve for x and y ?
x+y =20
0.12x+0.07y = 0.10*20

anonymous · Answer

am I supposed to put it in slope intercept form to solve for x and y?

hartnn · Answer

you can start by using substitution method
from 1st equation
y = 20 -x 
substitute this 'y' in 2nd equation

0.12x +0.07(20-x) = 2
can u get x from this?

anonymous · Answer

okay.. I got 0.12x + 1.4 = 2

hartnn · Answer

what about the 
0.07*(-x) term ?

anonymous · Answer

would I subtract 1.4 - 0.12 to get x?

hartnn · Answer

0.12x +0.07(20-x) = 2

0.12x + 0.07 * 20 - 0.07*x = 2 
0.12x + 1.4 - 0.07x = 2

hartnn · Answer

x (0.12 -0.07)  = 2-1.4

hartnn · Answer

x(0.05) = 0.6 

x= 0.6/ 0.05 = 60/5 = 12

hartnn · Answer

go through these steps and tell me if you have any doubt in any step

anonymous · Answer

so the answer would be A?

hartnn · Answer

YES.

anonymous · Answer

lol im sorry math is my worst subject.. it takes me awhile to get it :/

hartnn · Answer

no problem, glad you got it :)

anonymous · Answer

Thank you! (:

hartnn · Answer

welcome ^_^