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 that restaurant need to make 20 gallons of a lemonade mixture that is 10% sugar?

12 gallons of the 12% lemonade and 8 gallons of the 7% lemonade.
10 gallons of the 12% lemonade and 10 gallons of the 7% lemonade.
8 gallons of the 12% lemonade and 12 gallons of the 7% lemonade.
2 gallons of the 12% lemonade and 18 gallons of the 7% lemonade.

Answer 1

x = gallons of 12% sugar lemonade
y = gallons of 7% sugar lemonade
We can write 2 equations, now.
x + y = 20.......That's the easier one.
.12x + .07y = 0.1(20).....That's the other one
2 equations, 2 unknowns

Answer 2

I'm not sure I follow. I mean I get where you got the equation. But they all equal 20.

Answer 3

hello do u need help

Answer 4

Yes, I do.

Answer 5

well wat do u need help with

Answer 6

I don't quite understand the question I posted above. It seems as if I need to combine it to get the answer but I'm not fully sure.

Answer 7

that is egg zackuly wat u need to do

Answer 8

i be right bac hav to feed my 2 dogs it will take about 4 to 5 min...

Answer 9

They don't both equal 20. The 2nd one equals 0.1(20). That means 0.1 times 20...or 2.
The 2nd equation equals 2.

Answer 10

The way to solve a problem like this is by writing the two equations you were shown above. Then you need to solve the equations.

Here's a little explanation that may be of some help.

The first step is to pick two variables to represent the unknown amounts of the two lemonades.
Let the amount of 12% lemonade be x.
Let the amount of the 7% lemonade be y.

Since 20 liters of lemonade are being made,
x liters of 12% + y liters of 7% will equal 20 liters of 10%.

That gives you the equation

x + y = 20

Ok so far?

Answer 11

Yeah, I'm understanding so far.

Answer 12

im bac so do the variables first x+y -20

Answer 13

x+y = 20

Answer 14

Ok, since you have two unknowns, you need two equations.

Now we turn to the amount of sugar in the three types of lemonade to find a second equation.

Answer 15

A lemonade with 12% sugar has 0.12 times its amount in sugar.
The x gallons of 12% lemonade contain 0.12x sugar.
The y gallons of 7% lemonade contain 0.07y sugar.
Ok?

Answer 16

So it would be
0.12x + 0.07y = 20
right?

Answer 17

No, but close.

The amount of sugar is 0.12x and 0.07y from both lemonades.
They are added together, so
0.12x + 0.07y is correct.

The 10% resultant lemonade has a volume of 20 gal and a sugar concentration of 10%, so it has 0.10(20) sugar.

So now you have your second equation:

0.12x + 0.07y = 0.10(20)
or
0.12x + 0.07y = 2

Answer 18

Ohh I see

Answer 19

good but not quite, but you you have better help so im going to let him help you so good bye,talk to you latter if you still have questions just send me a message

Answer 20

@DIANTE Oh well thanks, and I will c:

Answer 21

k c ya

Answer 22

Now you have your two equations:

x + y = 20
0.12x + 0.07y = 2

Now you need to solve them simultaneously (as a system of equations).

Answer 23

wait i have 1 question wat grade r u n

Answer 24

im in the 9th

Answer 25

@DIANTE I am in 9th also.

@mathstudent55 Don't I have to use subtraction on both sides?

Answer 26

yes

Answer 27

its a 2 step equation

Answer 28

Start by multiplying the entire second equation by 100 to get rid of the decimals.

Answer 29

You get this:

x + y = 20
12x + 7y = 200

Answer 30

Now multiply the first equation by -7.
Then add it to the second equation.

Answer 31

mathstudent55 u r good at this wat grade r u in

Answer 32

-7x - 7y = -140 (first eq multiplied by -7)
12x + 7y = 200
-------------- (now add equations)

5x = 60

Solve for x:

x = 12

Now use the first original equation to solve for y:

x + y = 20
12 + y = 20
y = 8

The answer is 12 gal 12% lemonade + 8 gal 7% lemonade.

Answer 33

Oh now I understand how you got it. Thank you so much!

Answer 34

what school do u go to

Answer 35

You're welcome.

Answer 36

Connections

Answer 37

in GA

Answer 38

Yes, why?

Answer 39

I live in GA I go 2 Langston Hughes High school

Answer 40

Oh that's cool

Answer 41

i no right

Answer 42

well im bout to help someone else

Answer 43

That Connexus Cheating.