Question

Am I wrong if so why and how? (high not middle clicked wrong one)

Answer 1

Sean want to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice that is 30% lemon juice 70% lime juice to make 7 gallons of the 50%lemon/50%lime juice mixture?

0.5gallons


1gallons



2gallons



2.5 gallons

Answer 2

i think its 2

Answer 3

@Compassionate @tkhunny @nincompoop

Answer 4

tk what do you think?

Answer 5

Equate the Lemon Juice

X = Starting Quantity
Y = Additional Quantity

30% * X + 100% Y = 50% (X+Y)

And we know X+Y = 7

Equate the Lime Juice

X = Starting Quantity
Y = Additional Quantity

70% * X + 0% Y = 50% (X+Y)

And we know X+Y = 7

Answer 6

ok

Answer 7

I don't know. I didn't solve the either equation. Why do you believe it to be 2?

Answer 8

i calculated it and it came out to 2 but i believe im incorrect....

Answer 9

@tkhunny

Answer 10

can you at least tell me if im right or wrong?

Answer 11

@phi can you help

Answer 12

we have to solve a system of equations.
There are two parts to doing this:
1) figure out the equations
2) solve the equations

tk did step 1

now you can try to do step 2

Answer 13

how im totally confused

Answer 14

See if this makes sense:
we have an unknown amount of 30% lemon/70% lime. call this amount x

what fraction of that is lemon? any idea?

Answer 15

uhm would it be some where around 3/5?

Answer 16

How about with real numbers.
say you had 100 gallons of 30% lemon / 70% lime
any idea how many gallons of the 100 is lemon ?

Answer 17

no

Answer 18

ok, how about this different problem:
you have 100 gallons of 50% lemon and 50% lime
how many of the 100 gallons is lemon. any idea ?

Answer 19

50

Answer 20

so that would be 30

Answer 21

yes, 50 gallons.

and yes 30 gallons for the first problem

the "thought" is
30% of 100 means 30/100 * 100 or 0.30 * 100
(we can write 30% as either a fraction 30/100 or as a decimal 0.30)
we then multiply

so 10% of 20 would be 0.10*20 = 2
or 10/100 * 20 = 1/10 * 20 = 2
(or use a calculator)

ok so far?

Answer 22

yes so now what?

Answer 23

now back to 30% lemon/70% lime and we have x gallons of it

we use the same thought: the amount of lemon is 30% of x
and we do the same thing:

0.30*x or 0.3x
or 30x/100
the decimals are easier to type

so 0.3x is the number of gallons of lemon juice in the 30/70 stuff.

Answer 24

yes

Answer 25

next , we add 100% lemon juice.
we don't know how much that is, so we give it a name "y"
we add y gallons of pure lemon juice.
how much lemon juice will we have?
can you take a stab at writing that down ?

Answer 26

in other words, we start with 0.3x of lemon juice and add y gallons

Answer 27

i have been

Answer 28

how do we show 0.3x added to y ?

Answer 29

0,3x+y

Answer 30

0.3x*

Answer 31

yes.

next, we remember x is the number of gallons of juice (both lemon and lime)
and we pour in y gallons (of lemon)
how many gallons total do we have ?

Answer 32

30%?

Answer 33

no, don't think percent.

just imagine you have a bucket with x gallons of juice
and you pour in y more gallons
how many gallons total is in the bucket ?

Answer 34

30

Answer 35

I want you to think:
x+y
we start with x gallons and add y more gallons

Answer 36

70?

Answer 37

no, we can't do numbers. we have to use the letters
all we know (so far) is we have x+y gallons of juice

but we are told
50%lemon/50%lime juice
this new mixture is 50% lemon juice

how much lemon juice is in the (x+y) gallons ?

Answer 38

50

Answer 39

50% of (x+y)

Answer 40

?

Answer 41

can you imagine having "x" gallons of juice
and adding "y" gallons?
does that make sense or is it confusing ?

Answer 42

x+y

Answer 43

and if I said that 50% of that (x+y) is lemon, how do we write that ?

Answer 44

50+50?

Answer 45

you change the 50% to a decimal
and you multiply it times (x+y)
can you do that ?

Answer 46

0.3x+y

Answer 47

we are now doing
0.5*(x+y)
that is the amount of lemon juice in the new solution

and we know
0.3x+y is also the amount of lemon juice

they are equal amounts, so we write
0.3x+y= 0.5(x+y)
do you know how to "distribute" the 0.5 on the right side ?

Answer 48

no

Answer 49

0.5(x+y) means multiply 0.5 times x and multiply 0.5 times y
try it

Answer 50

ok phi i have to go thank you for every thing sorry for have to cut this short once again thank you for the help :) i have already fanned you but here is a medal

Answer 51

thank you!